Greedy Randomized and Maximal Weighted Residual Kaczmarz Methods with Oblique Projection

2021/06/25 by Wang Fang, Wang, Fang, Weiguo Li +5
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2106.13606

openalex publication_date 2021/06/25 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

For solving large-scale consistent linear system, we combine two efficient row index selection strategies with Kaczmarz-type method with oblique projection, and propose a greedy randomized Kaczmarz method with oblique projection (GRKO) and the maximal weighted residual Kaczmarz method with oblique projection (MWRKO) . Through those method, the number of iteration steps and running time can be reduced to a greater extent to find the least-norm solution, especially when the rows of matrix A are close to linear correlation. Theoretical proof and numerical results show that GRKO method and MWRKO method are more effective than greedy randomized Kaczmarz method and maximal weighted residual Kaczmarz method respectively.

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