A Greedy Two-Subspace Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

doi:10.11908/j.issn.0253-374x.21054

Home > Archive>Volume 49, Issue 10, 2021 >1473-1483. DOI:10.11908/j.issn.0253-374x.21054

A Greedy Two-Subspace Randomized Kaczmarz Method for Solving Large Sparse Linear Systems
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                        10.11908/j.issn.0253-374x.21054
                    
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                        JING Yanfei1JING Yanfei
School of Mathematical Sciences， University of Electronic Science and Technology of China， Chengdu 611731， China
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LI Caixia1LI Caixia
School of Mathematical Sciences， University of Electronic Science and Technology of China， Chengdu 611731， China
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HU Shaoliang2HU Shaoliang
CAEP Software Center for High Performance Numerical Simulation， Beijing 100088， China
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Affiliation:1.School of Mathematical Sciences， University of Electronic Science and Technology of China， Chengdu 611731， China;2.CAEP Software Center for High Performance Numerical Simulation， Beijing 100088， China
Clc Number:O241.6
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Abstract:

Based on an effective greedy probability criterion for selecting two working rows from a coefficient matrix， a greedy two-subspace randomized Kaczmarz method for solving large sparse linear systems is proposed. The theoretical analysis shows that this method converges to the minimal-norm solution of consistent linear systems， and the convergence factor of the method is smaller than that of the original two-subspace randomized Kaczmarz method. The numerical experiments show that this method is superior to the original two-subspace randomized Kaczmarz method from the point of view of solution performance.

Key words:two-subspace projection method;randomized Kaczmarz method;large sparse linear systems;convergence analysis

Reference

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JING Yanfei, LI Caixia, HU Shaoliang. A Greedy Two-Subspace Randomized Kaczmarz Method for Solving Large Sparse Linear Systems[J].同济大学学报(自然科学版),2021,49(10):1473~1483

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Received:March 19,2021
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Online: October 18,2021
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