Greedy Randomized and Maximal Weighted Residual Kaczmarz Methods with Oblique Projection

Greedy Randomized and Maximal Weighted Residual Kaczmarz Methods with Oblique Projection | 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 Greedy Randomized and Maximal Weighted Residual Kaczmarz Methods with Oblique Projection Fang Wang, Weiguo Li, Wendi Bao, Li Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-704730/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Jan, 2022 Read the published version in Mathematical Biosciences and Engineering → Version 1 posted You are reading this latest preprint version Abstract For solving large-scale consistent linear system, a greedy randomized Kaczmarz method with oblique projection and a maximal weighted residual Kaczmarz method with oblique projection are proposed. By using oblique projection, these two methods greatly reduce the number of iteration steps and running time to find the minimum norm solution, especially when the rows of matrix A are close to linear correlation. Theoretical proof and numerical results show that the greedy randomized Kaczmarz method with oblique projection and the maximal weighted residual Kaczmarz method with oblique projection are more effective than the greedy randomized Kaczmarz method and the maximal weighted residual Kaczmarz method respectively. Applied Mathematics Oblique projection Convergence property Kaczmarz method Correlation Large linear system Full Text Cite Share Download PDF Status: Published Journal Publication published 01 Jan, 2022 Read the published version in Mathematical Biosciences and Engineering → 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-704730","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":42991890,"identity":"9dff0dbf-dbe3-4138-88d1-4276a0729ab3","order_by":0,"name":"Fang Wang","email":"","orcid":"","institution":"China University of Petroleum Huadong - Qingdao Campus","correspondingAuthor":false,"prefix":"","firstName":"Fang","middleName":"","lastName":"Wang","suffix":""},{"id":42991891,"identity":"2499a80b-16b6-4b0e-ba8b-f559ca589bcd","order_by":1,"name":"Weiguo Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVRIiWNgGAWjYBACPmYg8QHCNiBOCxtQC+MM0rQAMTMPaVrYeYxf27bdkWdgb94mwVBzhxiH8ZhZ57Y9M2zgOVYmwXDsGTFaeLcZ57YdTmCQyDGTYGw4TKQWS5AW+TfEa9n8mBFsCw/RWvi/Mface2bYxpNWbJFwjAgt/PzHkj/8KLsjz89+eOONDzVEaAFZJMHAcAAcQQwJRGkAxuQHkJZRMApGwSgYBTgBAJchMPPTxD/9AAAAAElFTkSuQmCC","orcid":"","institution":"China University of Petroleum Huadong","correspondingAuthor":true,"prefix":"","firstName":"Weiguo","middleName":"","lastName":"Li","suffix":""},{"id":42991892,"identity":"28c7ca8b-f3a6-4a32-96b9-6ff78000d6a0","order_by":2,"name":"Wendi Bao","email":"","orcid":"","institution":"China University of Petroleum Huadong - 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