样条函数基本理论(第3版)(英文版)

本书是一部全面介绍单变量和张量积样条函数理 论的经典著作，为便于读者理解，书中呈现了样条理 论在诸多领域的应用，其中包括近似理论，计算机辅 助几何设计，曲线和曲面设计与拟合，图像处理，微 分方程的数值解，强调了该理论在商业和生物科学中 的应用也日益广泛。本书主要面向应用分析、数值分 析、计算科学和工程领域的研究生和科学工作者，也 可作为样条理论、近似理论和数值分析等应用数学专 业课教材或教学参考书。

Preface Preface to the 3rd Edition Chapter Ⅰ 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