Recursive interpolation algorithm: A formalism for solving systems of linear equations .2. Iterative methods

被引:13
作者
Messaoudi, A [1 ]
机构
[1] UNIV SCI & TECH LILLE FLANDRES ARTOIS,UFR IEEA M3,LAB ANAL NUMER & OPTIMISAT,F-59655 VILLENEUVE DASCQ,FRANCE
关键词
recursive interpolation algorithm; iterative methods;
D O I
10.1016/S0377-0427(96)00071-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper presents a simple unifying algorithm for solving systems of linear equations. Solving a system of linear equations will be interpreted as an interpolation problem. This new approach led us to a general algorithm called the recursive interpolation algorithm RIA. In Part I we gave the connection between this algorithm and known direct methods; in this part the truncated and the restarted versions of the RIA will be given. We will also show how to choose two free sets of parameters in the RIA for recovering some iterative methods.
引用
收藏
页码:31 / 53
页数:23
相关论文
共 30 条
[1]  
[Anonymous], 1965, Mathematics of computation, DOI DOI 10.1090/S0025-5718-1965-0198670-6
[2]  
[Anonymous], 1989, ABS PROJECTION ALGOR
[3]   A TAXONOMY FOR CONJUGATE-GRADIENT METHODS [J].
ASHBY, SF ;
MANTEUFFEL, TA ;
SAYLOR, PE .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (06) :1542-1568
[4]   A BLACK-BOX GENERALIZED CONJUGATE-GRADIENT SOLVER WITH INNER ITERATIONS AND VARIABLE-STEP PRECONDITIONING [J].
AXELSSON, O ;
VASSILEVSKI, PS .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1991, 12 (04) :625-644
[5]   A GENERALIZED CONJUGATE-GRADIENT, LEAST-SQUARE METHOD [J].
AXELSSON, O .
NUMERISCHE MATHEMATIK, 1987, 51 (02) :209-227
[7]   OTHER MANIFESTATIONS OF THE SCHUR COMPLEMENT [J].
BREZINSKI, C .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 111 :231-247
[8]   RECURSIVE INTERPOLATION, EXTRAPOLATION AND PROJECTION [J].
BREZINSKI, C .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1983, 9 (04) :369-376
[9]  
CONCUS P, 1976, SPARSE MATRIX COMPUT
[10]  
Daniel J. W., 1967, SIAM J NUMER ANAL, V4, P10