Solving ill-conditioned linear algebraic systems by the dynamical systems method (DSM)

2007/05/28 by N. S. Hoang, А. Г. Рамм, Hoang, N. S. +1 · 3 citations
Computer Science · Mathematics · #65F10 #65F22 #Algebra over a field #Algebraic number #Applied mathematics #Computer science #Dynamical systems theory #FOS: Mathematics #Linear system #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Physics #Pure mathematics #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.0705.4074

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2007/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An iterative scheme for the Dynamical Systems Method (DSM) is given such that one does not have to solve the Cauchy problem occuring in the application of the DSM for solving ill-conditioned linear algebraic systems. The novelty of the algorithm is that the algorithm does not have to find the regularization parameter a by solving a nonlinear equation. Numerical experiments show that DSM competes favorably with the Variational Regularization.

Citations

• An Introduction to the Mathematical Theory of Inverse Problems

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