A least squares approach for saddle point problems

Saddle point linear systems arise in many applications in computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. In this paper, we present a least-squa...

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Published in:Japan journal of industrial and applied mathematics 2023, Vol.40 (1), p.95-107
Main Authors: Karaduman, Gul, Yang, Mei, Li, Ren-Cang
Format: Article
Language:English
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Applications of Mathematics
Computational Mathematics and Numerical Analysis
Dynamical systems
Iterative methods
Least squares method
Linear systems
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Saddle points
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Li, Ren-Cang
description Saddle point linear systems arise in many applications in computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. In this paper, we present a least-squares approach to solve saddle point linear systems. The basic idea is to construct a projection matrix and transform a given saddle point linear system to a least-squares problem and then solve the least-squares problem by an iterative method such as LSMR: an iterative method for sparse least-squares problems. The proposed method rivals LSMR applied to the original problem in simplicity and ease to use. Numerical experiments demonstrate that the new iterative method is efficient and converges fast
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source Springer Nature
subjects Applications of Mathematics
Computational Mathematics and Numerical Analysis
Dynamical systems
Iterative methods
Least squares method
Linear systems
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Saddle points
title A least squares approach for saddle point problems
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