Subroutines and exercises for the computer solution of problems involving matrices, integrals, differential equations, spline functions, zeros and extrema of functions, least squares, and Monte Carlo techniques. Intended primarily for a course in numerical computing, this text can be used as supplement to a more theoretical text in a numerical analysis course. The programs have been carefully written so that they easily may be used on a wide variety of computers with little or no modification (from the dustjacket) FORTRAN subroutines. Includes - Introd & bibliography; Floating-Point Computation; Random Number generation & Monte Carlo methods; Optimization; Singular Value Decomposition; Interpolation; more. Cover......Page __sk_0000.djvu Copyright......Page __sk_0002.djvu Contents......Page __sk_0003.djvu Preface......Page __sk_0006.djvu 1 Introduction......Page __sk_0009.djvu 1.1 Bibliography......Page __sk_0010.djvu 1.2 About the programs in this book......Page __sk_0015.djvu Problems......Page __sk_0016.djvu 2.1 Floating-point numbers......Page __sk_0018.djvu 2.2 Calculation of machine epsilon......Page __sk_0021.djvu 2.3 An example of round-off error......Page __sk_0022.djvu 2.4 Instability of certain algorithms......Page __sk_0024.djvu 2.5 Sensitivity of certain problems......Page __sk_0025.djvu 2.6 Solving quadratic equations......Page __sk_0028.djvu Problems......Page __sk_0031.djvu 3 Linear Systems of Equations......Page __sk_0038.djvu 3.1 Linear systems for stored matrices......Page __sk_0040.djvu 3.2 Condition of a matrix......Page __sk_0049.djvu 3.3 Subroutines DECOMP and SOLVE......Page __sk_0056.djvu 3.4 Large, sparse systems......Page __sk_0064.djvu Problems......Page __sk_0066.djvu 4 Interpolation......Page __sk_0071.djvu 4.1 Polynomial interpolation......Page __sk_0072.djvu 4.2 Evaluation of polynomials......Page __sk_0076.djvu 4.3 An example, Runge's function......Page __sk_0077.djvu 4.4 Spline interpolation......Page __sk_0078.djvu 4.5 Subroutines SPLINE and SEVAL......Page __sk_0084.djvu Problems......Page __sk_0088.djvu 5 Numerical Integration......Page __sk_0092.djvu 5.1 The rectangle and trapezoid rules......Page __sk_0093.djvu 5.2 Spline quadrature......Page __sk_0097.djvu 5.3 Simpson's rule......Page __sk_0099.djvu 5.4 Adaptive quadrature routines......Page __sk_0100.djvu 5.5 Subroutine QUANC8......Page __sk_0105.djvu Problems......Page __sk_0114.djvu 6.1 The problem to be solved......Page __sk_0118.djvu 6.2 Numerical solutions......Page __sk_0120.djvu 6.3 Errors......Page __sk_0122.djvu 6.4 Methods......Page __sk_0127.djvu 6.5 Stiff equations......Page __sk_0131.djvu 6.6 Boundary value problems......Page __sk_0134.djvu 6.7 Choice of a subroutine......Page __sk_0135.djvu 6.8 Subroutine RKF45......Page __sk_0137.djvu Problems......Page __sk_0156.djvu 7.1 Transcendental equations-real roots......Page __sk_0164.djvu 7.2 Subroutine ZEROIN......Page __sk_0169.djvu 7.3 Transcendental equations-complex roots......Page __sk_0175.djvu 7.4 Zeros of polynomials......Page __sk_0176.djvu 7.5 Nonlinear systems of equations......Page __sk_0177.djvu Problems......Page __sk_0179.djvu 8 Optimization......Page __sk_0186.djvu 8.1 One-dimensional optimization......Page __sk_0187.djvu 8.2 Subroutine FMIN......Page __sk_0190.djvu 8.3 Optimization in many dimensions......Page __sk_0196.djvu Problems......Page __sk_0198.djvu 9.1 Least squares data fitting......Page __sk_0200.djvu 9.2 Orthogonality and the SVD......Page __sk_0209.djvu 9.3 Applications......Page __sk_0215.djvu 9.4 Computing the decomposition......Page __sk_0226.djvu 9.5 Subroutine SVD......Page __sk_0235.djvu Problems......Page __sk_0244.djvu 10 Random Number Generation and Monte Carlo Methods......Page __sk_0248.djvu 10.1 Generation of uniformly distributed numbers......Page __sk_0249.djvu 10.2 Subroutine URAND......Page __sk_0253.djvu 10.3 Sampling from other distributions......Page __sk_0255.djvu Problems......Page __sk_0256.djvu References......Page __sk_0258.djvu Index......Page __sk_0265.djvu Introduction -- Floating-point Computation -- Linear Systems Of Equations -- Interpolation -- Numerical Integration -- Initial Value Problems In Ordinary Differential Equations -- Solution Of Nonlinear Equations -- Optimization -- Least Squares And The Singular Value Decomposition -- Random Number Generation And Monte Carlo Methods. George E. Forsythe, Michael A. Malcolm, Cleve B. Moler. Includes Index. Bibliography: P. 250-255.
