Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control | 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 Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control Muhammed Yusuf Waziri, Naziru Idris Bala, Abubakar Sani Halilu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3512228/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 article presents a multi-step algorithm for solving a system of nonlinear equations using a double direction approach with application to motion control. In order to offer a useful derivative-free technique, the acceleration parameter is calculated to rougthly approximate the Jacobian matrix. With the aid of an inexact line search approach, the step-length was calculated. In addition, the proposed method is proving to be globally convergent under some appropriate conditions. Numerical experiment for some large-scale benchmark test problems reported in 1 this article shows the efficiency of the suggested methods compared with the current methods in the literature. System of Nonlinear Equations Acceleration parameter Multi-step iterative scheme Jacobian Matrix Global convergence and motion control 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. 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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-3512228","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":247438874,"identity":"121355f1-cefb-4c6f-addb-c2eee29ad397","order_by":0,"name":"Muhammed Yusuf Waziri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYNACAwYeIMnG8LEByGQAY6K0MLMxziReCxgwszHzEqNFd0aO4ccfBfdkGMTOH3tsu+OwMQN78zYJxh21OLWY3cgxlpAwKOZhkE5mN849c9iMgedYmQTjmeN4tORukDAwSABpYZPObTtswyCRYybB2HYMn5bNPxJgWixBWuTfENSyTeIATAtjG9BhEjwgLTW4tZx5/82yAaiFTTrZTLL3TLoxG09asUVi2wHcWo6nJd/88SfBnl868ZnEzx3Whv3shzfe+NhWh1MLg0AChGaDCYAZCQyHcWvhx+ECPLaMglEwCkbBSAMAsZVLduMNVT4AAAAASUVORK5CYII=","orcid":"","institution":"Bayero University Kano","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Muhammed","middleName":"Yusuf","lastName":"Waziri","suffix":""},{"id":247438875,"identity":"2e5a7b71-2262-4997-8beb-ecad4c4e4eec","order_by":1,"name":"Naziru Idris Bala","email":"","orcid":"","institution":"Kano University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Naziru","middleName":"Idris","lastName":"Bala","suffix":""},{"id":247438876,"identity":"5cc5a7f2-9f2c-473b-a3c9-b8a3bbdb69bd","order_by":2,"name":"Abubakar Sani Halilu","email":"","orcid":"","institution":"Sule Lamido University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Abubakar","middleName":"Sani","lastName":"Halilu","suffix":""}],"badges":[],"createdAt":"2023-10-30 14:44:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3512228/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3512228/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51368699,"identity":"515a92ca-3be0-4e2a-99e1-82dd2e93ea4e","added_by":"auto","created_at":"2024-02-20 11:14:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":448647,"visible":true,"origin":"","legend":"","description":"","filename":"HMADD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3512228/v1_covered_375da0a6-dad1-443b-992f-673169ba9105.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control","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":"System of Nonlinear Equations, Acceleration parameter, Multi-step iterative scheme, Jacobian Matrix, Global convergence and motion control","lastPublishedDoi":"10.21203/rs.3.rs-3512228/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3512228/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This article presents a multi-step algorithm for solving a system of nonlinear equations using a double direction approach with application to motion control. 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