New implementation of the Lanczos method in linear problems

Papadrakakis, M; Smerou, S

dc.contributor.author	Papadrakakis, M	en
dc.contributor.author	Smerou, S	en
dc.date.accessioned	2014-03-01T01:07:46Z
dc.date.available	2014-03-01T01:07:46Z
dc.date.issued	1990	en
dc.identifier.issn	0029-5981	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10159
dc.subject	lanczos method	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Computers, Digital - Computational Methods	en
dc.subject.other	Lanczos Algorithm	en
dc.subject.other	Linear Problems	en
dc.subject.other	Tridiagonal Matrix	en
dc.subject.other	Mathematical Techniques	en
dc.title	New implementation of the Lanczos method in linear problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/nme.1620290110	en
heal.identifier.secondary	http://dx.doi.org/10.1002/nme.1620290110	en
heal.language	English	en
heal.publicationDate	1990	en
heal.abstract	The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this paper a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right-hand sides. The versions of the method proposed in the past treat the right-hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.	en
heal.publisher	JOHN WILEY & SONS LTD	en
heal.journalName	International Journal for Numerical Methods in Engineering	en
dc.identifier.doi	10.1002/nme.1620290110	en
dc.identifier.isi	ISI:A1990CJ13000008	en
dc.identifier.volume	29	en
dc.identifier.issue	1	en
dc.identifier.spage	141	en
dc.identifier.epage	159	en