样条实用指南 修订本 英文版 作者：（美）布尔 著 出版时间： 2008年版 内容简介 《样条函数实用指南（修订版）》是著名数学家Carl de Boor的《样条函数实用指南》（1978）的修订版。原版本许多错误在修订版中得到了全面纠正。尤其是第九章到第十一章作了较大的修改，B-样条理论是直接建立在不依赖于均差的递归关系。这使得节点插入成为一个提供B-样条序列保形特性简单证明的强有力工具。本书的章节安排详略得当，重点突出，有利于读者学习理解。第一章简要讲述了多项式插值，特别是均差理论。第二章介绍了初步的多项式逼近论知识，并为讲述分段多项式函数做准备。只想了解样条函数大体知识的读者可以略过随后的四章。它们主要讲述了分段线性逼近、分段立方插值以及抛物型样条插值。第七、八章讲述了任意序的分段多项式函数的计算处理。第九、十、十一章介绍了B-样条。余下的几章介绍了各种应用，几乎都涉及到B-样条。每章后面都附有习题，供读者练习和加深理解，并且附有不少图形和程序。本书讲解透彻，但某些基本知识被略去，要求读者有较好的数值逼近、几何等的基础。本书为全英文版。 目录 Preface Notation I Polynomial Interpolation Polynomial Interpolation:Lagrange form Polynomial Interpolation:Divided differences and Newton Form Divided difference table Example:Osculatory interpolation to the logarithm Evaluation of the Newton form Example:COmputing the derivatives of a polynomial in Newton form Other polynomial forms and conditions Problems II Limitations of Polynomial Approximation Uniform spacing of data can have bad consquences Chebyshev sites are good Runge example with Chebyshev sites Squareroot example Interpolation at Chebyshev sites is nearly optimal The distance form polynomials Problems III Piecewise Linear Approximation Broken line interpolation Borken line interpolation is nearly optimal Least-squares approximation by broken lines Good meshes Problems IV Piecewise Cubic Interpolation Piecewise cubic Hermite interpolation Runge example continued Piecewise cubic Bessel interpolation Akimas interpolation Cubic spline interpolation Boundary conditions Problems V Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error Problems VI Parablolic Spline Interpolation Problems VII A Representation for Piecewise Polynomial Functions VIII The Spaces II and the Truncated Power Basis IX The Representation of PP Functions by B-Splines X The Stable Evaluation of B-Splines and Sploines XI The B-Spline Series Control Points and Knot Insertion XII Local Spline Approximation and the Distance from Splines XIII Spline Interpolation XIV Smoothing and Least-Squares APproximation XV The Numerical Solution of an Ordinary Differential Equation by Collocation XVI Taut Splines Periodic Splines Cardinal SAplines and the APproximation of Curves XVII Surface Approximation by Tensor Products Postscript on Things Not Covered Appendix:Fortran Programs Bibliography INdex
