Survey of quasi-Newton methods with reduced storage

Papadrakakis, M; Pantazopoulos, G

dc.contributor.author	Papadrakakis, M	en
dc.contributor.author	Pantazopoulos, G	en
dc.date.accessioned	2014-03-01T01:09:14Z
dc.date.available	2014-03-01T01:09:14Z
dc.date.issued	1993	en
dc.identifier.issn	0029-5981	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10871
dc.subject	quasi-newton method	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Approximation theory	en
dc.subject.other	Computational methods	en
dc.subject.other	Iterative methods	en
dc.subject.other	Linearization	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Loading variation	en
dc.subject.other	Post critical equilibrium paths	en
dc.subject.other	Preconditioned truncated Lanczos method	en
dc.subject.other	Quasi Newton methods	en
dc.subject.other	Updating formula	en
dc.subject.other	Numerical methods	en
dc.title	Survey of quasi-Newton methods with reduced storage	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/nme.1620360910	en
heal.identifier.secondary	http://dx.doi.org/10.1002/nme.1620360910	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	A family of non-linear solution methods is investigated based on limited-memory quasi-Newton updates. Depending upon the number of updates and the updating formula, a number of solution schemes may be constructed such as the conjugate- and secant-Newton methods, the conventional and modified Newton-Raphson methods and a variety of quasi-Newton updates. Under the proposed implementation, the preconditioned truncated Lanczos method is used for the solution of the linearized problem in each non-linear iteration. The complete factorization of the stiffness matrix is avoided and large-scale problems can be solved efficiently both in terms of computing time and storage. The non-linear iterative scheme is properly modified to account for loading variation inside the increment in order to be able to trace post-critical equilibrium paths.	en
heal.publisher	JOHN WILEY & SONS LTD	en
heal.journalName	International Journal for Numerical Methods in Engineering	en
dc.identifier.doi	10.1002/nme.1620360910	en
dc.identifier.isi	ISI:A1993LA75200009	en
dc.identifier.volume	36	en
dc.identifier.issue	9	en
dc.identifier.spage	1573	en
dc.identifier.epage	1596	en