
Accession Number : ADA115406
Title : Iterative Solution of Indefinite Symmetric Systems by Methods Using Orthogonal Polynomials over Two Disjoint Intervals.
Descriptive Note : Technical rept.,
Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
Personal Author(s) : Saad,Y
PDF Url : ADA115406
Report Date : 12 Oct 1981
Pagination or Media Count : 53
Abstract : It is shown in this paper that certain orthogonal polynomials over two disjoint intervals can be particularly useful for solving large symmetric indefinite linear systems or for finding a few interior eigenvalues of a large symmetric matrix. There are several advantages of the proposed approach over the techniques which are based upon the polynomials having the least uniform norm in two intervals. While a theoretical comparison will show that the norms of the minimal polynomial of degree n in the least squares sense differs from the minimax polynomial of the same degree by a factor not exceeding 2(n+1)to the 0.5 power, the least squares polynomials are by far easier to compute and to use thanks to their three term recurrence relation. A number of suggestions will be made for the problem of estimating the optimal parameters and several numerical experiments will be reported. (Author)
Descriptors : *Eigenvalues, *Polynomials, Iterations, Least squares method, Linear systems, Orthogonality, Chebyshev polynomials
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE