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...

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Bibliographische Detailangaben

1. Verfasser:	Saad, Yousef (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	[New Haven, Conn.] 1981
Schriftenreihe:	Yale University <New Haven, Conn.> / Department of Computer Science: Research report 212
Schlagworte:	Orthogonal polynomials Chebyshev polynomials Eigenvalues Iterations Least squares method Linear systems Orthogonality Polynomials Statistics and Probability
Zusammenfassung:	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).
Beschreibung:	51 Bl.