Computer methods for mathematical computations

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