On the extended randomized multiple row method for solving linear least-squares problems

Abstract

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple row method to solve a given overdetermined and inconsistent linear system and analyze its computational complexities at each iteration. We prove that the proposed method can linearly converge in the mean square to the least-squares solution with a minimum Euclidean norm. Several numerical studies are presented to corroborate our theoretical findings. The real-world applications, such as image reconstruction and large noisy data fitting in computer-aided geometric design, are also presented for illustration purposes.

References in corpus (5)

• Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method
• Randomized Extended Kaczmarz for Solving Least-Squares
• Randomized Iterative Methods for Linear Systems
• Generalized Row-Action Methods for Tomographic Imaging
• On Block Accelerations of Quantile Randomized Kaczmarz for Corrupted Systems of Linear Equations