标题: 谈谈计算数学(转自校内) [打印本页] 作者: mzszrj 时间: 2010-1-23 09:06 标题: 谈谈计算数学(转自校内) 虽然不是我写的,但我觉得很好,希望与大家分享。以下的内容转自校内:* i* |6 `+ z d3 k8 _* X4 D
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从计算数学的字面来看,应该与计算机有密切的联系,也强调 7 U% ~6 h# B- k8 X( i了实践对于计算数学的重要性。也许Parlett教授的一段话能6 ~% Q' T5 Z- B0 u/ @: _$ z0 k
最好地说明这个问题: 6 @, u. N) A" v0 V1 Z3 { $ F1 @# Y5 m/ j9 qHow could someone as brilliant as von Neumann think3 E0 X( B, Z: u, @+ g& u; I
hard about a subject as mundane as triangular factoriz " H1 r% d* c% ?" [' l) `% K-ation of an invertible matrix and not perceive that,6 z# A! Q( q& Q. H1 g; o
with suitable pivoting, the results are impressively 5 A5 s# `6 A5 [5 Q3 `8 ]. g: Vgood? Partial answers can be suggested-lack of hands-on , `4 ^3 Z1 o' a: s, G; m. g8 o, I" _experience, concentration on the inverse rather than on 5 ~' S5 |( D+ V! f2 t: h8 x8 Vthe solution of Ax = b -but I do not find them adequate.7 a* A0 F/ g. _0 M9 A
Why did Wilkinson keep the QR algorithm as a backup to a/ H( D. W0 p% d0 A. H
Laguerre-based method for the unsymmetric eigenproblem. d$ `7 k$ q1 g* P% Z
for at least two years after the appearance of QR? Why! A! i; G' f( j
did more than 20 years pass before the properties of / [. I3 m5 f" l& q# k" B2 g7 kthe Lanczos algorithm were understood? I believe that , k2 H7 {! w/ @* A: z/ l, G& |the explanation must involve the impediments to / ^" x6 z6 O+ B U# Lcomprehension of the effects of finite-precision 6 t0 j" s1 z# e5 Warithmetic.(引自www.siam.org/siamnews/11-03/matrix.pdf)2 K7 u8 ]4 I/ a1 g- a