樣條函數基本理論 第3版
作 者: (美)L.L.舒梅克(Larry L.Schumaker) 著
定 價: 109
出?版?社: 世界圖書出版公司
出版日期: 2019年10月01日
頁 數: 582
裝 幀: 平裝
ISBN: 9787519253578
●Preface
Preface to the 3rd Edition
Chapter 1 Introduction
1.1 Approximation Problems
1.2 Polynomials
1.3 Piecewise Polynomials
1.4 Spline Functions
1.5 Function Classes and Computers
1.6 Historical Notes
Chapter 2 Preliminaries
2.1 Function Classes
2.2 Taylor Expansions and the Green's Function
2.3 Matrices and Determinants
2.4 Sign Changes and Zeros
2.5 Tchebycheff Systems
2.6 Weak Tchebycheff Systems
2.7 Divided Differences
2.8 Moduli of Smoothness
2.9 The K-Functional
2.10 n-Widths
2.11 Periodic Functions
2.12 Historical Notes
2.13 Remarks
Chapter 3 Polynomials
3.1 Basic Properties
3.2 Zeros and Determinants
3.3 Variation-Diminishing Properties
3.4 Approximation Power of Polynomials
3.5 Whitney-Type Theorems
3.6 The Inflexibility of Polynomials
3.7 Historical Notes
3.8 Remarks
Chapter 4 Polynomial Splines
4.1 Basic Properties
4.2 Construction of a Local Basis
4.3 B-Splines
4.4 Equally Spaced Knots
4.5 The Perfect B-Spline
4.6 Dual Bases
4.7 Zero Properties
4.8 Matrices and Determinants
4.9 Variation-Diminishing Properties
4.10 Sign Properties of the Green's Function
4.11 Historical Notes
4.12 Remarks
Chapter 5 Computational Methods
5.1 Storage and Evaluation
5.2 Derivatives
5.3 The Piecewise Polynomial Representation
5.4 Integrals
5.5 Equally Spaced Knots
5.6 Historical Notes
5.7 Remarks
Chapter 6 Approximation Power of Splines
6.1 Introduction
6.2 Piecewise Constants
6.3 Piecewise Linear Functions
6.4 Direct Theorems
6.5 Direct Theorems in Intermediate Spaces
6.6 Lower Bounds
6.7 n-Widths
6.8 Inverse Theory for p=∞
6.9 Inverse Theory for 1≤p＜∞
6.10 Historical Notes
6.11 Remarks
Chapter 7 Approximation Power of Splines (Free Knots)
7.1 Introduction
7.2 Piecewise Constants
7.3 Variational Moduli of Smoothness
7.4 Direct and Inverse Theorems
7.5 Saturation
7.6 Saturation Classes
7.7 Historical Notes
7.8 Remarks
Chapter 8 Other Spaces of Polynomial Spllnes
8.1 Periodic Splines
8.2 Natural Splines
8.3 g-Splines
8.4 Monosplines
8.5 Discrete Splines
8.6 Historical Notes
8.7 Remarks
Chapter 9 Tchebycheffian Splines
9.1 Extended Complete Tchebycheff Systems
9.2 A Green's Function
9.3 Tchebycheffian Spline Functions
9.4 Tchebycheffian B-Splines
9.5 Zeros of Tchebycheffian Splines
9.6 Determinants and Sign Changes
9.7 Approximation Power of T-Splines
9.8 Other Spaces of Tchebycheffian Splines
9.9 Exponential and Hyperbolic Splines
9.10 Canonical Complete Tchebycheff Systems
9.11 Discrete Tchebycheffian Splines
9.12 Historical Notes
Chapter 10 L-Splines
10.1 Linear Differential Operators
10.2 A Green's Function
10.3 L-Splines
10.4 A Basis of Tchebycheffian B-Splines
10.5 Approximation Power of L-Splines
10.6 Lower Bounds
10.7 Inverse Theorems and Saturation
10.8 Trigonometric Splines
10.9 Historical Notes
10.10 Remarks
Chapter 11 Generalized Splines
11.1 A General Space of Splines
11.2 A One-Sided Basis
11.3 Constructing a Local Basis
11.4 Sign Changes and Weak Tchebycheff Systems
11.5 A Nonlinear Space of Generalized Splines
11.6 Rational Splines
11.7 Complex and Analytic Splines
11.8 Historical Notes
Chapter 12 Tensor-Product Splines
12.1 Tensor-Product Polynomial Splines
12.2 Tensor-Product B-Splines
12.3 Approximation Power of Tensor-Product Splines
12.4 Inverse Theory for Piecewise Polynomials
12.5 Inverse Theory for Splines
12.6 Historical Notes
Chapter 13 Some Multidimensional Tools
13.1 Notation
13.2 Sobolev Spaces
13.3 Polynomials
13.4 Taylor Theorems and the Approximation Power of Polynomials
13.5 Moduli of Smoothness
13.6 The K-Functional
13.7 Historical Notes
13.8 Remarks
Supplement
References
New References
Index
內容簡介
本書是一部全面介紹單變量和張量積樣條函數理論的經典著作，為便於讀者理解，書中呈現了樣條理論在諸多領域的應用，其中包括近似理論，計算機輔助幾何設計，曲線和曲面設計與擬合，圖像處理，微分方程的數值解，強調了該理論在商業和生物科學中的應用也日益廣泛。本書主要面向應用分析、數值分析、計算科學和工程領域的研究生和科學工作者，也可作為樣條理論、近似理論和數值分析等應用數學專業課教材或教學參考書。
