Numerical Computation 2 Methods, Software, and Analysis [Paperback]

This book is the second part of a modern, two-volume introduction to numerical computation, which strongly emphasizes software aspects. It can serve as a textbook for courses on numerical analysis, particularly for engineers. The book can also be used as a reference book and it includes an extensive bibliography. The author is a well-known specialist in numerical analysis who was involved in the creation of the software package QUADPACK.This book is the second part of a modern, two-volume introduction to numerical computation, which strongly emphasizes software aspects. It can serve as a textbook for courses on numerical analysis, particularly for engineers. The book can also be used as a reference book and it includes an extensive bibliography. The author is a well-known specialist in numerical analysis who was involved in the creation of the software package QUADPACK.10 Best Approximation.- 10.1 Mathematical Foundations.- 10.2 Continuous Least Squares Approximation.- 10.2.1 Mathematical Foundations.- 10.2.2 Best Approximation with Orthogonality.- 10.2.3 The Normal Equations.- 10.2.4 The Approximation Error.- 10.2.5 Orthogonal Polynomials.- 10.3 Discrete Least Squares Approximation.- 10.3.1 Linear Least Squares Approximation.- 10.3.2 Nonlinear Least Squares Approximation.- 10.4 Uniform Best Approximation.- 10.4.1 Uniformly Best Approximating Polynomials.- 10.5 Approximation Algorithms.- 10.6 Approximation Software for Special Functions.- 10.6.1 Elementary Functions.- 10.6.2 Funpack.- 10.6.3 IMSL Libraries.- 10.6.4 NAG Libraries.- 11 The Fourier Transform.- 11.1 Background.- 11.2 Mathematical Foundations.- 11.2.1 Trigonometric Approximation.- 11.2.2 The Spectrum.- 11.3 Trigonometric Interpolation.- 11.4 Convolution.- 11.5 Manipulation of the Signal Spectrum.- 11.5.1 Case Study: The Filtering of a Noisy Signal.- 11.6 DFT Algorithms.- 11.6.1 The Fast Fourier Transform (FFT).- 11.6.2 FFT of Real Functions.- 11.6.3 FFT in Two or More Dimensions.- 11.7 FFT Software Packal#œ