ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES-中国期刊网

摘要 TheHermitianandskew-Hermitiansplitting(HSS)methodisanunconditionallyconvergentiterationmethodforsolvinglargesparsenon-Hermitianpositivedefinitesystemoflinearequations.BymakinguseoftheHSSiterationastheinnersolverfortheNewtonmethod,weestablishaclassofNewton-HSSmethodsforsolvinglargesparsesystemsofnonlinearequationswithpositivedefiniteJacobianmatricesatthesolutionpoints.ForthisclassofinexactNewtonmethods,twotypesoflocalconvergencetheoremsareprovedunderproperconditions,andnumericalresultsaregiventoexaminetheirfeasibilityandeffectiveness.Inaddition,theadvantagesoftheNewton-HSSmethodsovertheNewton-USOR,theNewton-GMRESandtheNewton-GCGmethodsareshownthroughsolvingsystemsofnonlinearequationsarisingfromthefinitedifferencediscretizationofatwo-dimensionalconvection-diffusionequationperturbedbyanonlinearterm.ThenumericalimplementationsalsoshowthataspreconditionersfortheNewton-GMRESandtheNewton-GCGmethodstheHSSiterationoutperformstheUSORiterationinbothcomputingtimeanditerationstep.

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ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES

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ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES

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