Dynamical Systems Method for solving ill-conditioned linear algebraic systems

2009/11/16 by Sapto Wahyu Indratno, А. Г. Рамм, Indratno, Sapto W. +1
Computer Science · Mathematics · Physics and Astronomy · #15A12 #47A52 #65F05 #65F22 #Advanced Optimization Algorithms Research #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0911.3065

openalex publication_date 2009/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. This paper also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330 (2007),1338-1346, and proves convergence of the solution obtained by the iterative scheme.

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