Improved quasi-Newton methods for large nonlinear problems

Papadrakakis, Manolis; Balopoulos, Victor

dc.contributor.author	Papadrakakis, Manolis	en
dc.contributor.author	Balopoulos, Victor	en
dc.date.accessioned	2014-03-01T01:08:23Z
dc.date.available	2014-03-01T01:08:23Z
dc.date.issued	1991	en
dc.identifier.issn	0733-9399	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10457
dc.subject	Nonlinear Problem	en
dc.subject	quasi-newton method	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.other	Computer Programming--Algorithms	en
dc.subject.other	Mathematical Programming, Nonlinear	en
dc.subject.other	Mathematical Techniques--Nonlinear Equations	en
dc.subject.other	Mechanics--Computer Aided Analysis	en
dc.subject.other	Limited Memory Quasi Newton Methods	en
dc.subject.other	Preconditioning Matrices	en
dc.subject.other	Sparse Symmetric Jacobean Matrices	en
dc.subject.other	Structural Mechanics	en
dc.subject.other	Tangent Stiffness Matrices	en
dc.subject.other	Truncation	en
dc.subject.other	Structural Analysis	en
dc.title	Improved quasi-Newton methods for large nonlinear problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1061/(ASCE)0733-9399(1991)117:6(1201)	en
heal.identifier.secondary	http://dx.doi.org/10.1061/(ASCE)0733-9399(1991)117:6(1201)	en
heal.language	English	en
heal.publicationDate	1991	en
heal.abstract	In this work, schemes based on limited-memory quasi-Newton methods are investigated, as applied to solving large systems of nonlinear equations with sparse symmetric Jacobian matrices. Problems in mechanis typically give rise to such systems when the method of finite elements is employed to solve them. An attempt is made to develop algorithms that take advantage of sparsity and can effectively use a variable amount of storage according to the availability. The use of preconditioning matrices as initial approximations to the tangent stiffness matrix is suggested in order to accelerate convergence when the available high-speed storage exceeds the needs of purely vectorial methods but is not sufficient to house a full factorization of the tangent stiffness. The limited-memory quasi-Newton methods are also combined with the concept of truncation, based on a preconditioned conjugate gradient iterative solver of the linearized equations, to produce quite efficient algorithms.	en
heal.publisher	ASCE-AMER SOC CIVIL ENG	en
heal.journalName	Journal of Engineering Mechanics	en
dc.identifier.doi	10.1061/(ASCE)0733-9399(1991)117:6(1201)	en
dc.identifier.isi	ISI:A1991FN16900001	en
dc.identifier.volume	117	en
dc.identifier.issue	6	en
dc.identifier.spage	1201	en
dc.identifier.epage	1219	en