Vector sequence transformations. Methodology and applications to linear systems

被引：16
作者：
Brezinski, C [1 ]
机构：
[1] Univ Sci & Tech Lille Flandres Artois, Lab Anal Numer & Optimisat, F-59655 Villeneuve Dascq, France
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1998年 / 98卷 / 01期
关键词：
vector sequence transformations; convergence acceleration; systems of linear equations; Lanczos method;
D O I：
10.1016/S0377-0427(98)00119-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results. The connections to the general interpolation problem and to projections are discussed. Various particular cases are examined in more details. Applications to the solution of systems of linear equations will end the paper and, in particular, their relation with Lanczos method will be studied. Some numerical examples will be given. (C) 1998 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：149 / 175
页数：27
相关论文
共 54 条
[1]   Quasilinear sequence transformations [J].
Benazzouz, A .
NUMERICAL ALGORITHMS, 1997, 15 (3-4) :275-285
[2]  
BENCHIBOUN MD, 1992, ZASTOSOW MAT, V21, P407
[3]   A BREAKDOWN-FREE LANCZOS TYPE ALGORITHM FOR SOLVING LINEAR-SYSTEMS [J].
BREZINSKI, C ;
ZAGLIA, MR ;
SADOK, H .
NUMERISCHE MATHEMATIK, 1992, 63 (01) :29-38
[4]   Vector and matrix sequence transformations based on biorthogonality [J].
Brezinski, C ;
Zaglia, MR .
APPLIED NUMERICAL MATHEMATICS, 1996, 21 (04) :353-373
[5]   SEQUENCES OF TRANSFORMATIONS AND TRIANGULAR RECURSION SCHEMES, WITH APPLICATIONS IN NUMERICAL-ANALYSIS [J].
BREZINSKI, C ;
WALZ, G .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1991, 34 (03) :361-383
[6]   MATRIX AND VECTOR SEQUENCE TRANSFORMATIONS REVISITED [J].
BREZINSKI, C ;
SALAM, A .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1995, 38 :495-510
[7]   RECURSIVE INTERPOLATION, EXTRAPOLATION AND PROJECTION [J].
BREZINSKI, C .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1983, 9 (04) :369-376
[8]  
Brezinski C., 1975, Calcolo, V12, P317, DOI 10.1007/BF02575753
[9]   LANCZOS-TYPE ALGORITHMS FOR SOLVING SYSTEMS OF LINEAR-EQUATIONS [J].
BREZINSKI, C ;
SADOK, H .
APPLIED NUMERICAL MATHEMATICS, 1993, 11 (06) :443-473
[10]   COMPUTATION OF EIGENELEMENTS OF A MATRIX BY EPSILON-ALGORITHM [J].
BREZINSKI, C .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 11 (01) :7-20
123456