樣條實(shí)用指南

內(nèi)容概要

《樣條函數(shù)實(shí)用指南（修訂版）》是著名數(shù)學(xué)家Carl de Boor的《樣條函數(shù)實(shí)用指南》（1978）的修訂版。原版本許多錯(cuò)誤在修訂版中得到了全面糾正。尤其是第九章到第十一章作了較大的修改，B-樣條理論是直接建立在不依賴于均差的遞歸關(guān)系。這使得節(jié)點(diǎn)插入成為一個(gè)提供B-樣條序列保形特性簡單證明的強(qiáng)有力工具。    本書的章節(jié)安排詳略得當(dāng)，重點(diǎn)突出，有利于讀者學(xué)習(xí)理解。第一章簡要講述了多項(xiàng)式插值，特別是均差理論。第二章介紹了初步的多項(xiàng)式逼近論知識(shí)，并為講述分段多項(xiàng)式函數(shù)做準(zhǔn)備。只想了解樣條函數(shù)大體知識(shí)的讀者可以略過隨后的四章。它們主要講述了分段線性逼近、分段立方插值以及拋物型樣條插值。第七、八章講述了任意序的分段多項(xiàng)式函數(shù)的計(jì)算處理。第九、十、十一章介紹了B-樣條。余下的幾章介紹了各種應(yīng)用，幾乎都涉及到B-樣條。每章后面都附有習(xí)題，供讀者練習(xí)和加深理解，并且附有不少圖形和程序。本書講解透徹，但某些基本知識(shí)被略去，要求讀者有較好的數(shù)值逼近、幾何等的基礎(chǔ)。

書籍目錄

PrefaceNotationI 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  ProblemsII 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  ProblemsIII Piecewise Linear Approximation  Broken line interpolation  Borken line interpolation is nearly optimal  Least-squares approximation by broken lines  Good meshes  ProblemsIV Piecewise Cubic Interpolation  Piecewise cubic Hermite interpolation  Runge example continued  Piecewise cubic Bessel interpolation  Akimas interpolation  Cubic spline interpolation  Boundary conditions  ProblemsV Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error  ProblemsVI Parablolic Spline Interpolation  ProblemsVII A Representation for Piecewise Polynomial FunctionsVIII The Spaces II and the Truncated Power BasisIX The Representation of PP Functions by B-SplinesX The Stable Evaluation of B-Splines and SploinesXI The B-Spline Series Control Points and Knot InsertionXII Local Spline Approximation and the Distance from SplinesXIII Spline InterpolationXIV Smoothing and Least-Squares APproximationXV The Numerical Solution of an Ordinary Differential Equation by CollocationXVI Taut Splines Periodic Splines Cardinal SAplines and the APproximation of CurvesXVII Surface Approximation by Tensor ProductsPostscript on Things Not CoveredAppendix:Fortran ProgramsBibliographyINdex

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