The book has a twofold purpose: for one it provides an easy access to widely tested computer codes for over 130 numerical algorithms. At the same time it gives an informal introduction to the mathematical and computational principles of the underlying methods, as well as practical guidelines for their usage. 1 Computer Numbers, Error Analysis, Conditioning, Stability of Algorithms and Operations Count.- 2 Nonlinear Equations in One Variable.- 3 Roots of Polynomials.- 4 Direct Methods for Solving Systems of Linear Equations..- 5 Iterative Methods for Linear Systems.- 6 Systems of Nonlinear Equations.- 7 Eigenvalues and Eigenvectors of Matrices.- 8 Linear and Nonlinear Approximation.- 9 Polynomial and Rational Interpolation.- 10 Interpolating Polynomial Splines for Constructing Smooth Curves.- 11 Cubic Fitting Splines for Constructing Smooth Curves.- 12 Two-Dimensional Splines, Surface Splines, Bézier Splines, B-Splines.- 13 Akima and Renner Subsplines.- 14 Numerical Differentiation.- 15 Numerical Integration.- 16 Numerical Cubature.- 17 Initial Value Problems for Ordinary Differential Equations.- 18 Boundary Value Problems for Ordinary Differential Equations.- A Appendix: Standard FORTRAN 77 Subroutines.- A.1 Preface of the Appendix.- A.2 Information on Campus and Site Licenses, as well as on Other Software Packages.- A.3 Contents of the Enclosed CD.- of the Appendix.- A.4 FORTRAN 77 Subroutines.- B Bibliography.- Literature for Other Topics.- - Numerical Treatment of Partial Differential Equations.- - Finite Element Method.- C Index. The book has a twofold purpose: for one it provides an easy access to widely tested computer codes for over 130 numerical algorithms. At the same time it gives an informal introduction to the mathematical and computational principles of the underlying methods, as well as practical guidelines for their usage.
