Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0932.65040
Brezinski, C.; Redivo Zaglia, M.; Sadok, H.
New look-ahead Lanczos-type algorithms for linear systems. (English)
[J] Numer. Math. 83, No.1, 53-85 (1999). ISSN 0029-599X; ISSN 0945-3245/e

Authors' summary: A breakdown (due to a division by zero) can arise in the algorithms for implementing Lanczos' method because of the non-existence of some formal orthogonal polynomials or because the recurrence relationship used is not appropriate. Such a breakdown can be avoided by jumping over the polynomials involved. This strategy was already used in some algorithms such as the MRZ and its variants.\par In this paper, we propose new implementations of the recurrence relations of these algorithms which only need the storage of a fixed number of vectors, independent of the length of the jump. These new algorithms are based on Homer's rule and on a different way for computing the coefficients of the recurrence relationships. Moreover, these new algorithms seem to be more stable than the old ones and they provide better numerical results.\par Numerical examples and comparisons with other algorithms will be given.
[D.Braess (Bochum)]

MSC 2000:: *65F10 Iterative methods for linear systems

Keywords: look-ahead Lanczos-type algorithms; numerical stability of algorithms; numerical examples; breakdown; algorithms; recurrence relations; comparisons

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]