Lectures on Numerical mathematics
Lectures on Numerical mathematics
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数值数学讲座
DOI：
10.1007/bf02145584
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发表时间：
1991
影响因子：
2.1
通讯作者：
C. Brezinski
中科院分区：
文献类型：
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作者：
C. Brezinski
Heinz Rutishauser是数值算法的大师，因此，从本评论开始本节非常适合。他是著名的QD和LR算法的发现者，在现代意义上是数值分析的先驱之一。在他去世之前，他在1970年在德语中写道，本卷中包含的讲义。这些笔记由M.H.完成和编辑。在P. Henrici，P。l〜iuchli和H.R. Schwarz的协助下，W. Gautschi将他们翻译成英文，他们还用描述新发展并提供相关文献的注释补充了每一章。所涵盖的主题是：线性和非线性方程式系统的解决方案，最小二乘问题，多项式插值，正交，由Chebyshev系列以及Remez的算法，普通和部分微分方程的解决方案以及特征值问题。 QD-Algorithm上还有一个附录，以及计算机算术的公理处理。这是每位数字分析师都应该拥有的书，因为它包含了一位创造者的数值分析的主要思想。该书还可以作为科学计算和数值算法领域的学生的基本书籍。
Heinz Rutishauser was a master of numerical algorithms and, thus, it is very appropriate to begin this section with this review. He was the discoverer of the famous qd and LR algorithms and was one of the pioneers of numerical analysis in the modern sense of the term. Before his death, in 1970, he wrote in German the lecture notes contained in this volume. These notes were completed and edited by M.H. Gutknecht with the assistance of P. Henrici, P. L~iuchli and H.R. Schwarz and they were translated into English by W. Gautschi who also supplemented each chapter with notes describing the new developments and giving the relevant literature. The topics covered are: solution of systems of linear and nonlinear equations, least squares problems, polynomial interpolation, quadrature, approximation by Chebyshev series and by Remez' algorithm, solution of ordinary and partial differential equations and eigenvalue problems. There is also an appendix on the qd-algorithm and an axiomatic treatment of computer arithmetic. This is a book that every numerical analyst should have since it contains the main ideas which sustain numerical analysis by one of their creators. The book can also serve as a basic book for students in the field of scientific computing and numerical algorithms.