本书是著名数学家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。

Preface

Notation

I Polynomial Interpolation

II Limitations of Polynomial Appoximation

III Piecewise Linear Approximations

IV Piecewise Cubic Interpolation

V Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error

VI Parabolec Spline Interpolation

VII A Representation for Piecewise Polynomial Functions

VIII The Spaces

IX The Representation of PP Functions by B-Splines

X The Stable Evaluation of B-Splines and Splines

XI The B-Splines Series,Control Point,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 Splines and the Approximation of Curves

XVII Surface Approximation by Tensor Products

Appendix:Fortran Programs

Bibliography

Index