A Novel Iterative Approach for Absolute Value Equations

A Novel Iterative Approach for Absolute Value Equations | 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 Novel Iterative Approach for Absolute Value Equations Javed Iqbal, Taha Radwan, Aftab Iqbal, Muhammad Bilal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8655628/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 This paper studies a new iterative method for solving absolute value equations (AVEs). This new method is very efficient when the system matrix A has singular values greater than 1. The proposed method is a three-step method that converges to the solution very quickly. The linear convergence of the new method is proved under the condition that \(\:\:‖{A}^{-1}‖<\frac{1}{4}\) . Several numerical experiments show that the proposed method finds the solution in just two iterations with high accuracy of up to \(\:{\:\:10}^{-15}\) . Absolute value equation three-step method convergence Beam equation Numerical tests 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-8655628","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584493882,"identity":"6c5c09b6-c33b-45f6-b52b-69e571c9ee9f","order_by":0,"name":"Javed Iqbal","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Javed","middleName":"","lastName":"Iqbal","suffix":""},{"id":584493883,"identity":"df6161d4-fe06-4e4a-b83a-11eb641ba63b","order_by":1,"name":"Taha Radwan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYLACHiDmB7PYiFQNJiQbSNZicIBYLfYMvA8/vG2zyzM+nmPA8KHsMIN8+wFCtrAbS85tSy42O/PGgHHGucMMBmcSCGlhY5Dm3cacuO1GjgEzbxtQCwNhLcy/ebfVJ26eAdTyF6hFvv8BQS1sQFsOJ26QAGphBGphuEHIlsNsbJZz/x1PnHHmWcHBnnPpPAY3CNjC3t7GfOPNmerE/vbkjQ9+lFnLyfcTsIWBGc5KYDjAAI0oYgEhw0fBKBgFo2DEAgDekT4XzUsPvQAAAABJRU5ErkJggg==","orcid":"","institution":"Qassim University","correspondingAuthor":true,"prefix":"","firstName":"Taha","middleName":"","lastName":"Radwan","suffix":""},{"id":584493884,"identity":"1da62e0f-1bd7-42e4-b759-98c83a27561e","order_by":2,"name":"Aftab Iqbal","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Aftab","middleName":"","lastName":"Iqbal","suffix":""},{"id":584493885,"identity":"c5e8be65-5ea9-4ff8-99cf-4a4f0225626d","order_by":3,"name":"Muhammad Bilal","email":"","orcid":"","institution":"Abdul Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Bilal","suffix":""}],"badges":[],"createdAt":"2026-01-21 05:54:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8655628/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8655628/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105152147,"identity":"e8ebe1df-4776-418d-8c04-c7f04afb42c5","added_by":"auto","created_at":"2026-03-22 15:40:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":487756,"visible":true,"origin":"","legend":"","description":"","filename":"ThreeStepiterativeupdate1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8655628/v1_covered_782b740a-367e-485b-9cdf-fc3692c766f4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Iterative Approach for Absolute Value Equations","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":"Absolute value equation, three-step method, convergence, Beam equation, Numerical tests","lastPublishedDoi":"10.21203/rs.3.rs-8655628/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8655628/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper studies a new iterative method for solving absolute value equations (AVEs). This new method is very efficient when the system matrix A has singular values greater than 1. The proposed method is a three-step method that converges to the solution very quickly. The linear convergence of the new method is proved under the condition that\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:‖{A}^{-1}‖\u0026lt;\\frac{1}{4}\\)\u003c/span\u003e\u003c/span\u003e. 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