Numerical mathematics and scientific computation

Contents......Page 1
Introduction......Page 7
Common Ideas and Concepts......Page 8
Numerical Algorithms......Page 19
Numerical Solution of Differential Equations......Page 38
Monte Carlo Methods......Page 47
Linear Algebra and Matrix Computations......Page 57
Basic Concepts in Error Estimation......Page 81
Computer Number Systems......Page 87
Accuracy and Rounding Errors......Page 98
Error Propagation and Condition Numbers......Page 126
Some Basic Facts about Series......Page 149
Difference Operators and Operator Expansion......Page 190
Acceleration of Convergence......Page 242
Continued Fractions and Pade Approximants......Page 305
The Interpolation Problem......Page 323
Interpolation Formulas and Algorithms......Page 330
Interpolation where values of derivatives are used......Page 345
Spline Functions......Page 351
Polynomial Interpolation of Analytic Functions......Page 374
Trigonometric Interpolation and FFT......Page 384
Examples of Interpolation in Nonlinear Function Spaces......Page 387
Introduction......Page 389
Classical Quadrature Rules......Page 390
Special Transformations......Page 398
Multiple Integrals......Page 401
Introduction......Page 413
Fixed-Point Iteration......Page 419
Newton's Method......Page 424
Methods Based on Interpolation......Page 435
Attainable Accuracy and Multiple Roots......Page 444
Zero of Polynomials......Page 449
Minimizing a Scalar Function......Page 459
Appendix -  Guide to Literature......Page 473
Index......Page 478