Bibliography

1

M. Abramowitz and I. A. Stegun.
Handbook of Mathematical Functions.
Dover, New York, 1965.

2

F. S. Acton.
Numerical Methods That Work.
Math. Assoc. Amer., Washington, DC, 1990.
(reprint of 1970 edition).

3

F. S. Acton.
Real Computing Made Real.
Princeton University Press, Princeton, NJ, 1996.

4

J. H. Ahlberg, E. N. Nilson, and J. L. Walsh.
The Theory of Splines and Their Applications.
Academic, New York, 1967.

5

G. Alefeld and J. Herzberger.
Introduction to Interval Computations.
Academic, New York, 1983.

6

E. L. Allgower and K. Georg.
Numerical Continuation Methods.
Springer-Verlag, New York, 1990.

7

W. F. Ames.
Numerical Methods for Partial Differential Equations.
Academic, New York, 3d edition, 1992.

8

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen.
LAPACK User's Guide.
SIAM, Philadelphia, PA, 2d edition, 1995.

9

S. Anderson.
Random number generators.
SIAM Review, 32:221-251, 1990.

10

H. C. Andrews and C. L. Patterson.
Outer product expansions and their uses in digital image processing.
Amer. Math. Monthly, 82:1-13, 1975.

11

U. M. Ascher, R. M. Mattheij, and R. D. Russell.
Numerical Solution of Boundary Value Problems for Ordinary Differential Equations.
SIAM, Philadelphia, PA, 1995.
(reprint of 1988 edition).

12

K. Atkinson.
Elementary Numerical Analysis.
John Wiley & Sons, New York, 2d edition, 1993.

13

O. Axelsson.
Iterative Solution Methods.
Cambridge University Press, New York, 1994.

14

R. E. Bank.
PLTMG: A Software Package for Solving Elliptic Partial Differential Equations.
SIAM, Philadelphia, PA, 1994.

15

Y. Bard.
Nonlinear Parameter Estimation.
Academic, New York, 1970.

16

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst.
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods.
SIAM, Philadelphia, PA, 1994.

17

R. Bartels, J. Beatty, and B. Barsky.
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling.
Morgan Kaufmann, Los Altos, CA, 1987.

18

G. Barton.
Elements of Green's Functions and Propagation.
Oxford University Press, New York, 1989.

19

E. B. Becker, G. F. Carey, and J. T. Oden.
Finite Elements: An Introduction.
Prentice Hall, Englewood Cliffs, NJ, 1981.
(Texas Finite Element Series, Vol. 1).

20

A. Biran and M. Breiner.
MATLAB for Engineers.
Addison-Wesley, Reading, MA, 1995.

21

C. Bischof, A. Carle, P. Hovland, P. Khademi, and A. Maur.
ADIFOR 2.0 user's guide.
Technical Report ANL/MCS-TM-192, Argonne National Laboratory, Argonne, IL, 1995.

22

Å. Björck.
Numerical Methods for Least Squares Problems.
SIAM, Philadelphia, PA, 1996.

23

G. J. Borse.
Numerical Methods with MATLAB.
PWS Publishing Co., Boston, 1997.

24

J. F. Botha and G. F. Pinder.
Fundamental Concepts in the Numerical Solution of Partial Differential Equations.
John Wiley & Sons, New York, 1983.

25

P. Bratley, B. L. Fox, and L. E. Schrage.
A Guide to Simulation.
Springer-Verlag, New York, 2d edition, 1987.

26

K. E. Brenan, S. L. Campbell, and L. R. Petzold.
Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations.
SIAM, Philadelphia, PA, 1996.
(reprint of 1989 edition).

27

R. P. Brent.
Algorithms for Minimization without Derivatives.
Prentice Hall, Englewood Cliffs, NJ, 1973.

28

W. L. Briggs.
A Multigrid Tutorial.
SIAM, Philadelphia, PA, 1987.

29

W. L. Briggs and V. E. Henson.
The DFT: An Owner's Manual for the Discrete Fourier Transform.
SIAM, Philadelphia, PA, 1995.

30

E. O. Brigham.
The Fast Fourier Transform.
Prentice Hall, Englewood Cliffs, NJ, 1974.

31

E. O. Brigham.
The Fast Fourier Transform and Its Applications.
Prentice Hall, Englewood Cliffs, NJ, 1988.

32

P. Brinch Hansen.
Householder reduction of linear systems.
ACM Computing Surveys, 24(2):185-194, June 1992.

33

P. Brinch Hansen.
Studies in Computational Science.
Prentice Hall, Englewood Cliffs, NJ, 1995.

34

J. L. Buchanan and P. R. Turner.
Numerical Methods and Analysis.
McGraw-Hill, New York, 1992.

35

R. Bulirsch and J. Stoer.
Numerical treatment of ordinary differential equations by extrapolation methods.
Numer. Math., 8:1-13, 1966.

36

R. L. Burden and J. D. Faires.
Numerical Analysis.
PWS Publishing Co., Boston, 5th edition, 1993.

37

J. C. Butcher.
The Numerical Analysis of Ordinary Differential Equations.
John Wiley & Sons, New York, 1987.

38

G. D. Byrne and A. C. Hindmarsh.
Stiff ODE solvers: A review of current and coming attractions.
J. Comput. Phys., 70:1-62, 1987.

39

G. F. Carey and J. T. Oden.
Finite Elements: A Second Course.
Prentice Hall, Englewood Cliffs, NJ, 1983.
(Texas Finite Element Series, Vol. 2).

40

G. F. Carey and J. T. Oden.
Finite Elements: Computational Aspects.
Prentice Hall, Englewood Cliffs, NJ, 1984.
(Texas Finite Element Series, Vol. 3).

41

M. A. Celia and W. G. Gray.
Numerical Methods for Differential Equations.
Prentice Hall, Englewood Cliffs, NJ, 1992.

42

F. Chaitin-Chatelin and V. Frayssé.
Lectures on Finite Precision Computations.
SIAM, Philadelphia, PA, 1996.

43

S. C. Chapra and R. P. Canale.
Numerical Methods for Engineers.
McGraw-Hill, New York, 2d edition, 1988.

44

F. Chatelin.
Eigenvalues of Matrices.
John Wiley & Sons, New York, 1993.

45

W. Cheney and D. Kincaid.
Numerical Mathematics and Computing.
Brooks/Cole, Pacific Grove, CA, 3d edition, 1994.

46

B. Childs, M. Scott, J. W. Daniel, E. Denman, and P. Nelson, editors.
Codes for Boundary Value Problems in ODEs.
Springer-Verlag, New York, 1979.

47

E. Chong and S. Zak.
An Introduction to Optimization.
John Wiley & Sons, New York, 1996.

48

W. J. Cody.
The construction of numerical subroutine libraries.
SIAM Review, 16:36-46, 1974.

49

W. J. Cody et al.
A proposed radix and word-length independent standard for floating-point arithmetic.
IEEE Micro, 4(4):86-100, 1984.

50

T. F. Coleman and C. Van Loan.
Handbook for Matrix Computations.
SIAM, Philadelphia, PA, 1988.

51

S. D. Conte and C. de Boor.
Elementary Numerical Analysis.
McGraw-Hill, New York, 3d edition, 1980.

52

W. R. Cowell, editor.
Sources and Development of Mathematical Software.
Prentice Hall, Englewood Cliffs, NJ, 1984.

53

R. E. Crandall.
Projects in Scientific Computation.
Springer-Verlag, New York, 1994.

54

R. E. Crandall.
Topics in Advanced Scientific Computation.
Springer-Verlag, New York, 1996.

55

J. K. Cullum and R. A. Willoughby.
Lanczos Algorithms for Large Symmetric Eigenvalue Computations.
Birkhäuser, Boston, 1985.

56

G. Dahlquist and Å. Björck.
Numerical Methods.
Prentice Hall, Englewood Cliffs, NJ, 1974.

57

G. B. Dantzig.
Linear Programming and Extensions.
Princeton University Press, Princeton, NJ, 1963.

58

B. N. Datta.
Numerical Linear Algebra and Applications.
Brooks/Cole, Pacific Grove, CA, 1995.

59

A. J. Davies.
The Finite Element Method: A First Approach.
Oxford University Press, New York, 1980.

60

P. J. Davis.
Interpolation and Approximation.
Dover, New York, 1975.
(reprint of 1963 edition).

61

P. J. Davis and P. Rabinowitz.
Methods of Numerical Integration.
Academic, New York, 2d edition, 1984.

62

C. de Boor.
A Practical Guide to Splines.
Springer-Verlag, New York, 2d edition, 1984.

63

M. L. DeJong.
Introduction to Computational Physics.
Addison-Wesley, Reading, MA, 1991.

64

L. M. Delves and J. L. Mohamed.
Computational Methods for Integral Equations.
Cambridge University Press, New York, 1985.

65

J. W. Demmel, M. T. Heath, and H. A. van der Vorst.
Parallel numerical linear algebra.
Acta Numerica, 2:111-197, 1993.

66

J. Dennis, D. Gay, and R. Welsch.
An adaptive nonlinear least squares algorithm.
ACM Trans. Math. Software, 7:348-383, 1981.

67

J. E. Dennis and J. J. Moré.
Quasi-Newton methods, motivation and theory.
SIAM Review, 19:46-89, 1977.

68

J. E. Dennis and R. B. Schnabel.
Numerical Methods for Unconstrained Optimization and Nonlinear Equations.
SIAM, Philadelphia, PA, 1996.
(reprint of 1983 edition).

69

P. Deuflhard.
Recent progress in extrapolation methods for ordinary differential equations.
SIAM Review, 27:505-535, 1985.

70

P. Deuflhard and A. Hohmann.
Numerical Analysis: A First Course in Scientific Computation.
Walter de Gruyter, New York, 1995.

71

P. L. DeVries.
A First Course in Computational Physics.
John Wiley & Sons, New York, 1994.

72

P. Dierckx.
Curve and Surface Fitting with Splines.
Oxford University Press, New York, 1993.

73

J. Dongarra, J. DuCroz, I. S. Duff, and S. Hammarling.
A set of level-3 basic linear algebra subprograms.
ACM Trans. Math. Software, 16:1-28, 1990.

74

J. Dongarra, J. DuCroz, S. Hammarling, and R. J. Hanson.
An extended set of Fortran basic linear algebra subprograms.
ACM Trans. Math. Software, 14:1-32, 1988.

75

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart.
LINPACK User's Guide.
SIAM, Philadelphia, PA, 2d edition, 1979.

76

J. J. Dongarra, I. S. Duff, D. C. Sorensen, and H. A. van der Vorst.
Solving Linear Systems on Vector and Shared Memory Computers.
SIAM, Philadelphia, PA, 1990.

77

J. J. Dongarra, F. G. Gustavson, and A. Karp.
Implementing linear algebra algorithms for dense matrices on a vector pipeline machine.
SIAM Review, 26:91-112, 1984.

78

J. R. Dormand.
Numerical Methods for Differential Equations.
CRC Press, Boca Raton, FL, 1996.

79

C. C. Douglas.
Multigrid methods in science and engineering.
IEEE Comput. Sci. Engr., 3(4):55-68, 1996.

80

K. Dowd.
High Performance Computing.
O'Reilly & Associates, Sebastopol, CA, 1993.

81

I. S. Duff, A. M. Erisman, and J. K. Reid.
Direct Methods for Sparse Matrices.
Oxford University Press, New York, 1986.

82

P. Duhamel and M. Vetterli.
Fast Fourier transforms: A tutorial review and a state of the art.
Signal Processing, 19:259-299, 1990.

83

G. Engeln-Müllges and F. Uhlig.
Numerical Algorithms with C.
Springer-Verlag, New York, 1996.

84

H. Engels.
Numerical Quadrature and Cubature.
Academic, New York, 1980.

85

D. M. Etter.
Introduction to MATLAB for Engineers and Scientists.
Prentice Hall, Upper Saddle River, NJ, 1996.

86

D. M. Etter.
Engineering Problem Solving with MATLAB.
Prentice Hall, Upper Saddle River, NJ, 2d edition, 1997.

87

D. J. Evans, editor.
Software for Numerical Mathematics.
Academic, New York, 1974.

88

G. Evans.
Practical Numerical Integration.
John Wiley & Sons, New York, 1993.

89

V. Faber and T. Manteuffel.
Necessary and sufficient conditions for the existence of a conjugate gradient method.
SIAM J. Numer. Anal., 21:315-339, 1984.

90

S.-C. Fang and S. Puthenpura.
Linear Optimization and Extensions.
Prentice Hall, Englewood Cliffs, NJ, 1993.

91

R. W. Farebrother.
Linear Least Squares Computations.
Marcel Dekker, New York, 1987.

92

S. O. Fatunla.
Numerical Methods for Initial Value Problems in Ordinary Differential Equations.
Academic, New York, 1988.

93

A. V. Fiacco and G. P. McCormick.
Nonlinear Programming: Sequential Unconstrained Minimization Techniques.
SIAM, Philadelphia, PA, 1990.
(reprint of 1968 edition).

94

G. S. Fishman.
Monte Carlo: Concepts, Algorithms, and Applications.
Springer-Verlag, New York, 1996.

95

R. Fletcher.
Practical Methods of Optimization.
John Wiley & Sons, New York, 2d edition, 1987.

96

B. Fornberg.
A Practical Guide to Pseudospectral Methods.
Cambridge University Press, New York, 1996.

97

G. E. Forsythe, M. A. Malcolm, and C. B. Moler.
Computer Methods for Mathematical Computations.
Prentice Hall, Englewood Cliffs, NJ, 1977.

98

G. E. Forsythe and C. B. Moler.
Computer Solution of Linear Algebraic Systems.
Prentice Hall, Englewood Cliffs, NJ, 1967.

99

G. E. Forsythe and W. R. Wasow.
Finite Difference Methods for Partial Differential Equations.
John Wiley & Sons, New York, 1960.

100

L. Fosdick, E. Jessup, C. Schauble, and G. Domik.
An Introduction to High-Performance Scientific Computing.
The MIT Press, Cambridge, MA, 1995.

101

L. Fox.
The Numerical Solution of Two-Point Boundary Problems.
Dover, New York, 1990.
(reprint of 1957 edition).

102

R. W. Freund, G. H. Golub, and N. M. Nachtigal.
Iterative solution of linear systems.
Acta Numerica, 1:57-100, 1992.

103

F. N. Fritsch and R. E. Carlson.
Monotone piecewise cubic interpolation.
SIAM J. Numer. Anal., 17:238-246, 1980.

104

W. Gander and J. Hrebicek.
Solving Problems in Scientific Computing Using Maple and MATLAB.
Springer-Verlag, New York, 2d edition, 1995.

105

B. S. Garbow, J. M. Boyle, J. J. Dongarra, and C. B. Moler.
Matrix Eigensystem Routines: EISPACK Guide Extension.
Springer-Verlag, New York, 1972.

106

A. L. Garcia.
Numerical Methods for Physics.
Prentice Hall, Englewood Cliffs, NJ, 1994.

107

A. L. Garcia and C. Penland.
MATLAB Projects for Scientists and Engineers.
Prentice Hall, Upper Saddle River, NJ, 1996.

108

W. Gautschi.
ORTHPOL - a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software, 20:21-62, 1994.

109

D. M. Gay.
Subroutines for unconstrained minimization using a model/trust region approach.
ACM Trans. Math. Software, 9:503-534, 1983.

110

C. W. Gear.
Numerical Initial Value Problems in Ordinary Differential Equations.
Prentice Hall, Englewood Cliffs, NJ, 1971.

111

C. W. Gear.
Numerical solution of ordinary differential equations: Is there anything left to do?
SIAM Review, 23:10-24, 1981.

112

A. George and J. W.-H. Liu.
Computer Solution of Large Sparse Positive Definite Systems.
Prentice Hall, Englewood Cliffs, NJ, 1981.

113

C. F. Gerald and P. O. Wheatley.
Applied Numerical Analysis.
Addison-Wesley, Reading, MA, 5th edition, 1994.

114

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright.
User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming.
Technical Report SOL-86-2, Systems Optimization Laboratory, Stanford University, Stanford, CA, 1986.

115

P. E. Gill, W. Murray, and M. H. Wright.
Practical Optimization.
Academic, New York, 1981.

116

P. E. Gill, W. Murray, and M. H. Wright.
Numerical Linear Algebra and Optimization, volume 1.
Addison-Wesley, Reading, MA, 1991.

117

N. J. Giordano.
Computational Physics.
Prentice Hall, Englewood Cliffs, NJ, 1997.

118

R. Glassey.
Numerical Computation Using C.
Academic, New York, 1993.

119

D. Goldberg.
What every computer scientist should know about floating-point arithmetic.
ACM Computing Surveys, 18(1):5-48, March 1991.

120

D. Goldfarb.
Algorithms for unconstrained optimization: A review of recent developments.
In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proc. Symp. Appl. Math., pages 33-48. Amer. Math. Soc., 1993.

121

D. Goldfarb and M. J. Todd.
Linear programming.
In G. Nemhauser et al., editors, Optimization, pages 73-170. North-Holland, New York, 1989.

122

H. H. Goldstine.
A History of Numerical Analysis from the 16th through the 19th Century.
Springer-Verlag, New York, 1977.

123

G. H. Golub.
Numerical methods for solving linear least squares problems.
Numer. Math., 7:206-216, 1965.

124

G. H. Golub and D. P. O'Leary.
Some history of the conjugate gradient and Lanczos methods.
SIAM Review, 31:50-102, 1989.

125

G. H. Golub and J. M. Ortega.
Scientific Computing and Differential Equations.
Academic, New York, 2d edition, 1992.

126

G. H. Golub and C. F. Van Loan.
Matrix Computations.
Johns Hopkins University Press, Baltimore, MD, 3d edition, 1996.

127

G. H. Golub and J. H. Welsch.
Calculation of Gauss quadrature rules.
Math. Comp., 23:221-230, 1969.

128

D. Gottlieb and S. A. Orszag.
Numerical Analysis of Spectral Methods.
SIAM, Philadelphia, PA, 1977.

129

H. Gould and J. Tobochnik.
An Introduction to Computer Simulation Methods.
Addison-Wesley, Reading, MA, 2d edition, 1996.

130

R. J. Goult, R. F. Hoskins, J. A. Milner, and M. J. Pratt.
Computational Methods in Linear Algebra.
John Wiley & Sons, New York, 1974.

131

A. R. Gourlay and G. A. Watson.
Computational Methods for Matrix Eigenproblems.
John Wiley & Sons, New York, 1973.

132

T. A. Grandine.
The Numerical Methods Programming Projects Book.
Oxford University Press, New York, 1990.

133

A. Graps.
An introduction to wavelets.
IEEE Comput. Sci. Engr., 2(2):50-61, 1995.

134

G. K. Gupta, R. Sacks-Davis, and P. E. Tischer.
A review of recent developments in solving ODEs.
ACM Computing Surveys, 17:5-47, 1985.

135

B. Gustafsson, H.-O. Kreiss, and J. Oliger.
Time Dependent Problems and Difference Methods.
John Wiley & Sons, New York, 1995.

136

S. Haber.
Numerical evaluation of multiple integrals.
SIAM Review, 12:481-526, 1970.

137

W. Hackbusch.
Iterative Solution of Large Sparse Systems of Equations.
Springer-Verlag, New York, 1994.

138

L. A. Hageman and D. M. Young.
Applied Iterative Methods.
Academic, New York, 1981.

139

W. Hager.
Applied Numerical Linear Algebra.
Prentice Hall, Englewood Cliffs, NJ, 1988.

140

E. Hairer, S. Norsett, and G. Wanner.
Solving Ordinary Differential Equations.
Springer-Verlag, New York, 1987.

141

C. A. Hall and T. A. Porsching.
Numerical Analysis of Partial Differential Equations.
Prentice Hall, Englewood Cliffs, NJ, 1990.

142

G. Hämmerlin and K.-H. Hoffmann.
Numerical Mathematics.
Springer-Verlag, New York, 1991.
(translation of 1989 German edition).

143

J. M. Hammersley and D. C. Handscomb.
Monte Carlo Methods.
Chapman and Hall, New York, 1965.

144

R. W. Hamming.
Numerical Methods for Scientists and Engineeers.
Dover, New York, 2d edition, 1986.
(reprint of 1973 edition).

145

D. Hanselman and B. Littlefield.
Mastering MATLAB.
Prentice Hall, Upper Saddle River, NJ, 1996.

146

P. C. Hansen.
Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems.
Numerical Algorithms, 6:1-35, 1994.

147

D. W. Heermann.
Computer Simulation Methods in Theoretical Physics.
Springer-Verlag, New York, 1990.

148

M. A. Hennell and L. M. Delves, editors.
Production and Assessment of Numerical Software.
Academic, New York, 1980.

149

P. Henrici.
Discrete Variable Methods in Ordinary Differential Equations.
John Wiley & Sons, New York, 1962.

150

P. Henrici.
Elements of Numerical Analysis.
John Wiley & Sons, New York, 1964.

151

N. J. Higham.
A survey of condition number estimation for triangular matrices.
SIAM Review, 29:575-596, 1987.

152

N. J. Higham.
A survey of componentwise perturbation theory in numerical linear algebra.
In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proc. Symp. Appl. Math., pages 49-77. Amer. Math. Soc., 1993.

153

N. J. Higham.
Accuracy and Stability of Numerical Algorithms.
SIAM, Philadelphia, PA, 1996.

154

D. R. Hill.
Experiments in Computational Matrix Algebra.
Random House, New York, 1988.

155

T. Hopkins and C. Phillips.
Numerical Methods in Practice.
Addison-Wesley, Reading, MA, 1988.

156

A. S. Householder.
The Numerical Treatment of a Single Nonlinear Equation.
McGraw-Hill, New York, 1970.

157

B. B. Hubbard.
The World According to Wavelets.
A K Peters, Ltd., Wellesley, MA, 1996.

158

IEEE.
A proposed standard for floating-point arithmetic.
IEEE Computer, 14(3):51-62, March 1981.

159

IEEE.
IEEE standard 754-1985 for binary floating-point arithmetic.
SIGPLAN Notices, 22(2):9-25, 1987.
(see also IEEE Computer, March 1981).

160

E. Isaacson and H. B. Keller.
Analysis of Numerical Methods.
Dover, New York, 1994.
(reprint of 1966 edition).

161

A. Iserles.
A First Course in the Numerical Analysis of Differential Equations.
Cambridge University Press, New York, 1996.

162

D. Jacobs, editor.
Numerical Software: Needs and Availability.
Academic, New York, 1978.

163

P. Jarratt and D. Nudds.
The use of rational functions in the iterative solution of equations on a digital computer.
Computer J., 8:62-65, 1965.

164

M. A. Jenkins and J. F. Traub.
Zeros of a complex polynomial.
Comm. ACM, 15:97-99, 1972.

165

M. A. Jenkins and J. F. Traub.
Zeros of a real polynomial.
ACM Trans. Math. Software, 1:178-189, 1975.

166

A. Jennings and J. J. McKeown.
Matrix Computation.
John Wiley & Sons, New York, 2d edition, 1992.

167

D. C. Jespersen.
Multigrid methods for partial differential equations.
In G. H. Golub, editor, Studies in Numerical Analysis, pages 270-318. Math. Assoc. Amer., Washington, DC, 1984.

168

C. Johnson.
Numerical Solution of Partial Differential Equations by the Finite Element Method.
Cambridge University Press, New York, 1987.

169

D. C. Joyce.
Survey of extrapolation processes in numerical analysis.
SIAM Review, 13:435-488, 1971.

170

D. Kahaner, C. Moler, and S. Nash.
Numerical Methods and Software.
Prentice Hall, Englewood Cliffs, NJ, 1989.

171

G. Kaiser.
A Friendly Guide to Wavelets.
Birkhäuser, Boston, 1994.

172

M. H. Kalos and P. A. Whitlock.
Monte Carlo Methods.
John Wiley & Sons, New York, 1986.

173

W. J. Kaufmann and L. L. Smarr.
Supercomputing and the Transformation of Science.
Scientific American Library, New York, 1993.

174

H. B. Keller.
Numerical Methods for Two-Point Boundary-Value Problems.
Dover, New York, 1992.
(reprint of 1968 edition).

175

C. T. Kelley.
Iterative Methods for Linear and Nonlinear Equations.
SIAM, Philadelphia, PA, 1995.

176

W. J. Kennedy and J. E. Gentle.
Statistical Computing.
Marcel Dekker, New York, 1980.

177

D. Kincaid and W. Cheney.
Numerical Analysis.
Brooks/Cole, Pacific Grove, CA, 2d edition, 1996.

178

D. E. Knuth.
The Art of Computer Programming: Seminumerical Algorithms, volume 2.
Addison-Wesley, Reading, MA, 1969.

179

N. Köckler.
Numerical Methods and Scientific Computing.
Oxford University Press, New York, 1994.

180

S. E. Koonin and D. C. Meredith.
Computational Physics.
Addison-Wesley, Reading, MA, 1990.

181

I. Koren.
Computer Arithmetic Algorithms.
Prentice Hall, Englewood Cliffs, NJ, 1993.

182

A. R. Krommer and C. W. Ueberhuber.
Computational Integration.
SIAM, Philadelphia, PA, 1996.

183

P. K. Kythe.
Boundary Element Methods.
CRC Press, Boca Raton, FL, 1995.

184

J. D. Lambert.
Computational Methods in Ordinary Differential Systems.
John Wiley & Sons, New York, 1973.

185

J. D. Lambert.
Numerical Methods for Ordinary Differential Systems.
John Wiley & Sons, New York, 1991.

186

R. H. Landau.
A Project Approach to Computational Physical Science.
John Wiley & Sons, New York, 1997.

187

R. H. Landau and P. J. Fink.
A Scientist's and Engineer's Guide to Workstations and Supercomputers.
John Wiley & Sons, New York, 1993.

188

L. Lapidus and G. F. Pinder.
Numerical Solution of Partial Differential Equations in Science and Engineering.
John Wiley & Sons, New York, 1982.

189

L. Lapidus and J. Seinfeld.
Numerical Solution of Ordinary Differential Equations.
Academic, New York, 1971.

190

F. M. Larkin.
Root-finding by fitting rational functions.
Math. Comp., 35:803-816, 1980.

191

H. T. Lau.
A Numerical Library in C for Scientists and Engineers.
CRC Press, Boca Raton, FL, 1995.

192

C. L. Lawson and R. J. Hanson.
Solving Least Squares Problems.
SIAM, Philadelphia, PA, 1995.
(updated reprint of 1974 edition).

193

C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh.
Basic linear algebra subprograms for Fortran usage.
ACM Trans. Math. Software, 5:308-325, 1979.

194

R. J. LeVeque.
Numerical Methods for Conservation Laws.
Birkhäuser, Boston, 2d edition, 1992.

195

G. Lindfield and J. Penny.
Numerical Methods Using MATLAB.
Ellis Horwood, New York, 1995.

196

J. W. Longley.
Least Squares Computations Using Orthogonalization Methods.
Marcel Dekker, New York, 1984.

197

D. W. Lozier and F. W. J. Olver.
Numerical evaluation of special functions.
In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proc. Symp. Appl. Math., pages 79-125. Amer. Math. Soc., 1993.

198

D. G. Luenberger.
Linear and Nonlinear Programming.
Addison-Wesley, Reading, MA, 2d edition, 1984.

199

J. N. Lyness.
When not to use an automatic quadrature routine.
SIAM Review, 25:63-88, 1983.

200

J. N. Lyness and R. Cools.
A survey of numerical cubature over triangles.
In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proc. Symp. Appl. Math., pages 127-150. Amer. Math. Soc., 1993.

201

J. N. Lyness and J. J. Kaganove.
Comments on the nature of automatic quadrature routines.
ACM Trans. Math. Software, 2:65-81, 1976.

202

A. R. Magid.
Applied Matrix Models.
John Wiley & Sons, New York, 1985.

203

G. Marsaglia.
Random numbers fall mainly in the planes.
Proc. Nat. Acad. Sci., 61:25-28, 1968.

204

J. H. Mathews.
Numerical Methods.
Prentice Hall, Englewood Cliffs, NJ, 2d edition, 1992.

205

W. Miller.
The Engineering of Numerical Software.
Prentice Hall, Englewood Cliffs, NJ, 1984.

206

W. Miller and C. Wrathall.
Software for Roundoff Analysis of Matrix Algorithms.
Academic, New York, 1980.

207

A. R. Mitchell and D. F. Griffiths.
The Finite Difference Method in Partial Differential Equations.
John Wiley & Sons, New York, 1980.

208

C. B. Moler.
Matrix computations with Fortran and paging.
Comm. ACM, 15:268-270, 1972.

209

C. B. Moler and D. Morrison.
Singular value analysis of cryptograms.
Amer. Math. Monthly, 90:78-87, 1983.

210

C. B. Moler and C. F. Van Loan.
Nineteen dubious ways to compute the exponential of a matrix.
SIAM Review, 20:801-836, 1978.

211

R. E. Moore.
Interval Analysis.
Prentice Hall, Englewood Cliffs, NJ, 1966.

212

R. E. Moore.
Methods and Applications of Interval Analysis.
SIAM, Philadelphia, PA, 1979.

213

J. J. Moré.
The Levenberg-Marquardt algorithm: Implementation and theory.
In G. A. Watson, editor, Numerical Analysis, pages 105-116. Springer-Verlag, New York, 1977.

214

J. J. Moré, B. S. Garbow, and K. E. Hillstrom.
User guide for MINPACK-1.
Technical Report ANL-80-74, Argonne National Laboratory, Argonne, IL, 1980.

215

J. J. Moré and D. C. Sorensen.
Newton's method.
In G. H. Golub, editor, Studies in Numerical Analysis, pages 29-82. Math. Assoc. Amer., Washington, DC, 1984.

216

J. J. Moré and Stephen J. Wright.
Optimization Software Guide.
SIAM, Philadelphia, PA, 1993.

217

N. Morrison.
Introduction to Fourier Analysis.
John Wiley & Sons, New York, 1994.

218

K. W. Morton and D. F. Mayers.
Numerical Solution of Partial Differential Equations.
Cambridge University Press, New York, 1994.

219

B. A. Murtagh and M. A. Saunders.
MINOS 5.1 user's guide.
Technical Report SOL-83-20R, Systems Optimization Laboratory, Stanford University, Stanford, CA, January 1987.

220

S. Nakamura.
Numerical Analysis and Graphic Visualization with MATLAB.
Prentice Hall, Upper Saddle River, NJ, 1996.

221

S. G. Nash, editor.
A History of Scientific Computing.
ACM Press, New York, 1990.

222

S. G. Nash and A. Sofer.
Linear and Nonlinear Programming.
McGraw-Hill, New York, 1996.

223

H. Niederreiter.
Random Number Generation and Quasi-Monte Carlo Methods.
SIAM, Philadelphia, PA, 1992.

224

J. Nievergelt, J. C. Farrar, and E. M. Reingold.
Computer Approaches to Mathematical Problems.
Prentice Hall, Englewood Cliffs, NJ, 1974.

225

J. Nocedal.
Theory of algorithms for unconstrained optimization.
Acta Numerica, 1:199-242, 1992.

226

A. R. Omondi.
Computer Arithmetic Systems.
Prentice Hall, Englewood Cliffs, NJ, 1994.

227

J. M. Ortega.
Introduction to Parallel and Vector Solution of Linear Systems.
Plenum, New York, 1988.

228

J. M. Ortega.
Numerical Analysis: A Second Course.
SIAM, Philadelphia, PA, 1990.
(reprint of 1972 edition).

229

J. M. Ortega and W. C. Rheinboldt.
Iterative Solution of Nonlinear Equations in Several Variables.
Academic, New York, 1970.

230

A. M. Ostrowski.
Solution of Equations and Systems of Equations.
Academic, New York, 2d edition, 1966.

231

C. C. Paige and M. A. Saunders.
Solution of sparse indefinite systems of linear equations.
SIAM J. Numer. Anal., 12:617-629, 1975.

232

B. N. Parlett.
The Symmetric Eigenvalue Problem.
Prentice Hall, Englewood Cliffs, NJ, 1980.

233

E. Part-Enander, A. Sjoberg, B. Melin, and P. Isaksson.
MATLAB Handbook.
Addison-Wesley, Reading, MA, 1996.

234

V. Pereyra.
Finite difference solution of boundary value problems in ordinary differential equations.
In G. H. Golub, editor, Studies in Numerical Analysis, pages 243-269. Math. Assoc. Amer., Washington, DC, 1984.

235

L. Petzold.
Differential-algebraic systems are not ODEs.
SIAM J. Sci. Stat. Comput., 3:367-384, 1982.

236

M. Pickering.
An Introduction to Fast Fourier Transform Methods for Partial Differential Equations, with Aplications.
John Wiley & Sons, New York, 1986.

237

R. Piessens, E. deDoncker Kapenga, C. Uberhuber, and D. Kahaner.
QUADPACK: A Subroutine Package for Automatic Integration.
Springer-Verlag, New York, 1983.

238

R. Pratap.
Getting Started with MATLAB.
Saunders College Publishing, Fort Worth, TX, 1995.

239

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery.
Numerical Recipes.
Cambridge University Press, New York, 2d edition, 1992.

240

A. Ralston and P. Rabinowitz.
A First Course in Numerical Analysis.
McGraw-Hill, New York, 1978.

241

D. Redfern and C. Campbell.
The MATLAB Handbook.
Springer-Verlag, New York, 1996.

242

C. H. Reinsch.
Smoothing by spline functions.
Numer. Math., 10:177-183, 1967.

243

C. H. Reinsch.
Smoothing by spline functions II.
Numer. Math., 16:451-454, 1971.

244

J. R. Rice, editor.
Mathematical Software.
Academic, New York, 1971.

245

J. R. Rice, editor.
Mathematical Software III.
Academic, New York, 1977.

246

J. R. Rice.
Numerical Methods, Software, and Analysis.
Academic, New York, 2d edition, 1993.

247

J. R. Rice and R. F. Boisvert.
Solving Elliptic Problems Using ELLPACK.
Springer-Verlag, New York, 1985.

248

R. Richtmyer and K. W. Morton.
Difference Methods for Initial-Value Problems.
John Wiley & Sons, New York, 2d edition, 1967.

249

G. F. Roach.
Green's Functions.
Cambridge University Press, New York, 2d edition, 1982.

250

S. Roberts and J. Shipman.
Two-Point Boundary Value Problems: Shooting Methods.
Elsevier, New York, 1972.

251

R. Rubinstein.
Simulation and the Monte Carlo Method.
John Wiley & Sons, New York, 1981.

252

Y. Saad.
Numerical Methods for Large Eigenvalue Problems.
John Wiley & Sons, New York, 1992.

253

Y. Saad.
Iterative Methods for Sparse Linear Systems.
PWS Publishing Co., Boston, 1996.

254

W. E. Schiesser.
The Numerical Method of Lines Integration of Partial Differential Equations.
Academic, New York, 1991.

255

R. B. Schnabel, J. E. Koontz, and B. E. Weiss.
A modular system of algorithms for unconstrained minimization.
ACM Trans. Math. Software, 11:419-440, 1985.

256

L. L. Schumaker.
Spline Functions.
John Wiley & Sons, New York, 1981.

257

H. R. Schwarz.
Numerical Analysis: A Comprehensive Introduction.
John Wiley & Sons, New York, 1989.

258

H. R. Schwarz, H. Rutishauser, and E. Stiefel.
Numerical Analysis of Symmetric Matrices.
Prentice Hall, Englewood Cliffs, NJ, 1973.

259

L. F. Shampine.
What everyone solving differential equations numerically should know.
In I. Gladwell and D. K. Sayers, editors, Computational Techniques for Ordinary Differential Equations, pages 1-17. Academic, New York, 1980.

260

L. F. Shampine.
Numerical Solution of Ordinary Differential Equations.
Chapman and Hall, New York, 1994.

261

L. F. Shampine and R. C. Allen.
Numerical Computing: An Introduction.
W. B. Saunders, Philadelphia, PA, 1973.

262

L. F. Shampine, R. C. Allen, and S. Pruess.
Fundamentals of Numerical Computing.
John Wiley & Sons, New York, 1997.

263

L. F. Shampine and C. W. Gear.
A user's view of solving stiff ordinary differential equations.
SIAM Review, 21:1-17, 1979.

264

L. F. Shampine and M. K. Gordon.
Computer Solution of Ordinary Differential Equations.
W. H. Freeman, San Francisco, 1975.

265

L. F. Shampine, H. A. Watts, and S. M. Davenport.
Solving nonstiff ordinary differential equations--the state of the art.
SIAM Review, 18:376-411, 1976.

266

E. V. Shikin and A. I. Plis.
Handbook on Splines for the User.
CRC Press, Boca Raton, FL, 1995.

267

K. Sigmon.
MATLAB Primer.
CRC Press, Boca Raton, FL, 4th edition, 1994.

268

R. D. Skeel.
Equivalent forms of multistep methods.
Math. Comp., 33:1229-1250, 1979.

269

R. D. Skeel and J. B. Keiper.
Elementary Numerical Computing with Mathematica.
McGraw-Hill, New York, 1993.

270

I. H. Sloan and S. Joe.
Lattice Methods for Multiple Integration.
Oxford University Press, New York, 1994.

271

B. T. Smith, J. M. Boyle, Y. Ikebe, V. C. Klema, and C. B. Moler.
Matrix Eigensystem Routines: EISPACK Guide.
Springer-Verlag, New York, 2d edition, 1970.

272

G. D. Smith.
Numerical Solution of Partial Differential Equations.
Oxford University Press, New York, 3d edition, 1985.

273

R. L. Smith.
The MATLAB Project Book.
Prentice Hall, Upper Saddle River, NJ, 1997.

274

I. M. Sobol'.
A Primer for the Monte Carlo Method.
CRC Press, Boca Raton, FL, 1994.

275

H. Späth.
One Dimensional Spline Interpolation Algorithms.
A K Peters, Ltd., Wellesley, MA, 1995.

276

P. H. Sterbenz.
Floating-Point Computation.
Prentice Hall, Englewood Cliffs, NJ, 1974.

277

H. J. Stetter.
Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation.
In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proc. Symp. Appl. Math., pages 205-224. Amer. Math. Soc., 1993.

278

G. W. Stewart.
Introduction to Matrix Computations.
Academic, New York, 1973.

279

G. W. Stewart.
Afternotes on Numerical Analysis.
SIAM, Philadelphia, PA, 1996.

280

G. W. Stewart and T. G. Sun.
Matrix Perturbation Theory.
Academic, New York, 1990.

281

J. Stoer and R. Bulirsch.
Introduction to Numerical Analysis.
Springer-Verlag, New York, 2d edition, 1993.

282

G. Strang.
Introduction to Applied Mathematics.
Wellesley-Cambridge Press, Wellesley, MA, 1986.

283

G. Strang.
Linear Algebra and Its Applications.
W. B. Saunders, New York, 3d edition, 1988.

284

G. Strang.
Wavelets.
Amer. Scientist, 82:250-255, 1992.

285

G. Strang.
Introduction to Linear Algebra.
Wellesley-Cambridge Press, Wellesley, MA, 1993.

286

G. Strang and G. Fix.
An Analysis of the Finite Element Method.
Prentice Hall, Englewood Cliffs, NJ, 1973.

287

V. Strassen.
Gaussian elimination is not optimal.
Numer. Math., 13:354-356, 1969.

288

J. C. Strikwerda.
Finite Difference Schemes and Partial Differential Equations.
Chapman and Hall, New York, 1989.

289

A. H. Stroud.
Approximate Calculation of Multiple Integrals.
Prentice Hall, Englewood Cliffs, NJ, 1972.

290

A. H. Stroud and D. Secrest.
Gaussian Quadrature Formulas.
Prentice Hall, Englewood Cliffs, NJ, 1966.

291

W. H. Swann.
Direct search methods.
In W. Murray, editor, Numerical Methods for Unconstrained Optimization, pages 13-28. Academic, New York, 1972.

292

P. N. Swarztrauber.
Fast Poisson solvers.
In G. H. Golub, editor, Studies in Numerical Analysis, pages 319-370. Math. Assoc. Amer., Washington, DC, 1984.

293

C. Taswell and K. C. McGill.
Wavelet transform algorithms for finite-duration discrete-time signals.
ACM Trans. Math. Software, 20:398-412, 1994.

294

R. A. Thisted.
Elements of Statistical Computing.
Chapman and Hall, New York, 1988.

295

J. W. Thomas.
Numerical Partial Differential Equations, volume 1.
Springer-Verlag, New York, 1995.

296

W. J. Thompson.
Atlas for Computing Mathematical Functions.
John Wiley & Sons, New York, 1996.

297

J. F. Traub.
Iterative Methods for the Solution of Equations.
Prentice Hall, Englewood Cliffs, NJ, 1964.

298

L. N. Trefethen.
Three mysteries of Gaussian elimination.
SIGNUM Newsletter, 20(4):2-5, October 1985.

299

L. N. Trefethen and D. Bau.
Numerical Linear Algebra.
SIAM, Philadelphia, PA, 1997.

300

S. Van Huffel and J. Vandewalle.
The Total Least Squares Problem.
SIAM, Philadelphia, PA, 1991.

301

C. F. Van Loan.
Computational Frameworks for the Fast Fourier Transform.
SIAM, Philadelphia, PA, 1992.

302

C. F. Van Loan.
An Introduction to Computational Science and Mathematics.
Jones and Bartlett, Sudbury, MA, 1996.

303

C. F. Van Loan.
Introduction to Scientific Computing.
Prentice Hall, Upper Saddle River, NJ, 1997.

304

R. S. Varga.
Matrix Iterative Analysis.
Prentice Hall, Englewood Cliffs, NJ, 1962.

305

S. A. Vavasis.
Gaussian elimination with pivoting is P-complete.
SIAM J. Disc. Math., 2:413-423, 1989.

306

F. J. Vesely.
Computational Physics: An Introduction.
Plenum, New York, 1994.

307

E. L. Wachpress.
Iterative Solution of Elliptic Systems.
Prentice Hall, Englewood Cliffs, NJ, 1966.

308

R. Wait and A. R. Mitchell.
Finite Element Analysis and Applications.
John Wiley & Sons, New York, 1985.

309

J. S. Walker.
Fourier Analysis.
Oxford University Press, New York, 1988.

310

J. S. Walker.
Fast Fourier Transforms.
CRC Press, Boca Raton, FL, 2d edition, 1996.

311

D. S. Watkins.
Understanding the QR algorithm.
SIAM Review, 24:427-440, 1982.

312

D. S. Watkins.
Fundamentals of Matrix Computations.
John Wiley & Sons, New York, 1991.

313

D. S. Watkins.
Some prospectives on the eigenvalue problem.
SIAM Review, 35:430-471, 1993.

314

L. T. Watson, S. C. Billups, and A. P. Morgan.
HOMPACK: A suite of codes for globally convergent homotopy algorithms.
ACM Trans. Math. Software, 13:281-310, 1987.

315

H. J. Weaver.
Applications of Discrete and Continuous Fourier Analysis.
John Wiley & Sons, New York, 1983.

316

H. J. Weaver.
Theory of Discrete and Continuous Fourier Analysis.
John Wiley & Sons, New York, 1989.

317

P. Wesseling.
An Introduction to Multigrid Methods.
John Wiley & Sons, New York, 1992.

318

J. R. Westlake.
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations.
John Wiley & Sons, New York, 1968.

319

D. J. Wilde.
Optimum Seeking Methods.
Prentice Hall, Englewood Cliffs, NJ, 1964.

320

J. H. Wilkinson.
Error analysis of direct methods of matrix inversion.
J. ACM, 8:281-330, 1961.

321

J. H. Wilkinson.
Rounding Errors in Algebraic Processes.
Prentice Hall, Englewood Cliffs, NJ, 1963.

322

J. H. Wilkinson.
The Algebraic Eigenvalue Problem.
Oxford University Press, New York, 1965.

323

J. H. Wilkinson and C. Reinsch, editors.
Handbook for Automatic Computation, Linear Algebra, volume 2.
Springer-Verlag, New York, 1971.

324

G. M. Wing.
A Primer on Integral Equations of the First Kind.
SIAM, Philadelphia, PA, 1991.

325

S. M. Wong.
Computational Methods in Physics and Engineering.
Prentice Hall, Englewood Cliffs, NJ, 1992.

326

M. H. Wright.
Interior methods for constrained optimization.
Acta Numerica, 1:341-407, 1992.

327

M. H. Wright and S. Glassman.
Fortran subroutines to solve linear least squares problems and compute the complete orthogonal factorization.
Technical Report SOL-78-8, Systems Optimization Laboratory, Stanford University, Stanford, CA, April 1978.

328

D. M. Young.
Iterative Solution of Large Linear Systems.
Academic, New York, 1971.

329

D. M. Young and R. T. Gregory.
A Survey of Numerical Mathematics.
Dover, New York, 1988.
(reprint of 1972-73 edition).

330

J. L. Zachary.
Introduction to Scientific Programming: Computational Problem Solving Using Maple and C.
Springer-Verlag, New York, 1996.

331

S. Zhang and J. Jin.
Computation of Special Functions.
John Wiley & Sons, New York, 1996.

332

O. C. Zienkiewicz and R. L. Taylor.
The Finite Element Method.
McGraw-Hill, New York, 4th edition, 1989.

333

Z. Zlatev, J. Wasniewski, and K. Schaumburg.
Y12M: Solution of Large and Sparse Systems of Linear Algebraic Equations.
Springer-Verlag, New York, 1981.

334

D. Zwillinger, editor.
Standard Mathematical Tables and Formulae.
CRC Press, Boca Raton, FL, 30th edition, 1996.