Two-step relaxation Newton method for nonsymmetric algebraic Riccati equations arising from transport theory
type: Item
instance of: scholarly article
title: Two-step relaxation Newton method for nonsymmetric algebraic Riccati equations arising from transport theory
zbMATH Open document ID: 1184.65047
DOI: 10.1155/2009/783920
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45900
review text: Summary: We propose a new idea to construct an effective algorithm to compute the minimal positive solution of the nonsymmetric algebraic Riccati equations arising from transport theory. For a class of these equations, an important feature is that the minimal positive solution can be obtained by computing the minimal positive solution of a couple of fixed-point equations with vector form. Based on the fixed-point vector equations, we introduce a new algorithm, namely, two-step relaxation Newton, derived by combining two different relaxation Newton methods to compute the minimal positive solution. The monotone convergence of the solution sequence generated by this new algorithm is established. Numerical results are given to show the advantages of the new algorithm for the nonsymmetric algebraic Riccati equations in vector form.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5632542
zbMATH Keywords: algorithm
zbMATH Keywords: minimal positive solution
zbMATH Keywords: nonsymmetric algebraic Riccati equations
zbMATH Keywords: fixed-point equations
zbMATH Keywords: two-step relaxation Newton
zbMATH Keywords: monotone convergence
zbMATH Keywords: numerical results
Wikidata QID: Q58649489
author: Shulin Wu
author: Chengming Huang
MaRDI profile type: Publication
OpenAlex ID: W2101352184
cites work: Q4089129
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description: scientific article; zbMATH DE number 5632542