A simplified RHSS iteration method for saddle point problems

A simplified RHSS iteration method for saddle point problems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A simplified RHSS iteration method for saddle point problems yuqin bai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2650926/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Recently, Bai and Benzi [Regularized HSS iteration methods for saddlepoint linear systems, Bit Numer . Math ., 57 (2017) 287-311] have presented a class of regularized Hermitian and skew-Hermitian splitting methods to solve saddle point problems. In this paper, we establish a simplified RHSS (SRHSS) preconditioner which is much closer to the saddle point matrix than the RHSS preconditioner. We prove the convergence of the proposed method (SRHSS) under suitable restrictions on the iteration parameters. We also study the spectral properties of the preconditioned matrix and eigenvector distribution. Lastly, numerical experiments are carried out and experimental results show that the proposed SRHSS preconditoner method is feasible and effective. AMSC : 65F10; 65F15; 65F50 Saddle point problems preconditioning shift-splitting iterative method spectral properties Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2650926","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":181386454,"identity":"c8f8087e-d158-45e4-aa76-715e7607bad6","order_by":0,"name":"yuqin bai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYFACHgaGhAoJHn72xsaHH4jXcsZGTrLncLOxBNFaGNvSjA1mpLcJ8BCjweB47sEPD9gOJ26QfNjGIMFgJ6fbQEjLmXfJEgk8hxO3Sye2PShgSDY2O0BIy40cA4kEicOJO2cnthtIMBxI3EaEFuMfCQZAh9082CbBQ6QWM4mEBKD3bzASqUXyzLs0i4QDoEBOBAayARF+4Tuee/jmz3+gqDz+8OGHCjs5gloUDiSguJOAchCQb0ggqGYUjIJRMApGOgAA8DtJo2cbtjoAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"yuqin","middleName":"","lastName":"bai","suffix":""}],"badges":[],"createdAt":"2023-03-03 10:14:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2650926/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2650926/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":34344494,"identity":"abf188a0-3e26-441c-a42f-c5567fa4484d","added_by":"auto","created_at":"2023-03-16 09:44:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":203249,"visible":true,"origin":"","legend":"","description":"","filename":"AsimplifiedRHSSiterationmethodforsaddlepointproblems.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2650926/v1_covered.pdf"},{"id":33995291,"identity":"3f9479cf-7674-412a-a5e9-dcbe9c77a1eb","added_by":"auto","created_at":"2023-03-09 05:35:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":198825,"visible":true,"origin":"","legend":"","description":"","filename":"AsimplifiedRHSSiterationmethodforsaddlepointproblems.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2650926/v1/f29bc46aed0c7e89c32ef656.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A simplified RHSS iteration method for saddle point problems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Saddle point problems, preconditioning, shift-splitting, iterative method, spectral properties","lastPublishedDoi":"10.21203/rs.3.rs-2650926/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2650926/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecently, Bai and Benzi [Regularized HSS iteration methods for saddlepoint linear systems, \u003cem\u003eBit Numer\u003c/em\u003e. \u003cem\u003eMath\u003c/em\u003e., 57 (2017) 287-311] have presented a class of regularized Hermitian and skew-Hermitian splitting methods to solve saddle point problems. In this paper, we establish a simplified RHSS (SRHSS) preconditioner which is much closer to the saddle point matrix than the RHSS preconditioner. We prove the convergence of the proposed method (SRHSS) under suitable restrictions on the iteration parameters. We also study the spectral properties of the preconditioned matrix and eigenvector distribution. 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