On the theory of degenerate systems of ordinary differential equations
type: Item
instance of: scholarly article
title: On the theory of degenerate systems of ordinary differential equations
zbMATH Open document ID: 0856.34002
DOI: 10.1007/BF02112544
author: T. L. Shtykel'
published in: Siberian Mathematical Journal
publication date: 1997-02-19T00:00:00Z
review text: The system \(A\dot x(t)= Ix(t)+ f(t)\) is considered. A quasi-inverse matrix is introduced, using which solvability conditions in the form of algebraic relations are obtained. A uniqueness theorem for a solution is proved. An \(m\)-quasi-inverse matrix is involved. To calculate it an algorithm is proposed for stable determination of the subspace corresponding to the ``almost zero'' eigenvalues of the matrix. The construction of singular vectors of a matrix which is based on exhaustion of singular values provides guaranteed accuracy for results and better estimates considering former results. In this aspect the proposed algorithm differs from its prototype [see \textit{V. N. Kublanovskaya}, Zh. Vychisl. Mat. Mat. Fiz. 6, No. 4, 611-620 (1966; Zbl 0171.36001)]. Some examples of numerical tests are presented.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 65L15
zbMATH DE Number: 923571
zbMATH Keywords: degenerate system
zbMATH Keywords: solvability conditions
zbMATH Keywords: uniqueness
zbMATH Keywords: \(m\)-quasi-inverse matrix
zbMATH Keywords: algorithm
zbMATH Keywords: exhaustion of singular values
MaRDI profile type: Publication
cites work: Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients
cites work: Q3900330
cites work: Q4002602
cites work: Q3996786
cites work: Q3813196
cites work: An algorithm for numerical determination of the structure of a general matrix
cites work: Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
cites work: Q3210764
cites work: Q3994613
full work available at URL: https://doi.org/10.1007/bf02112544
OpenAlex ID: W2084018220
description: scientific article; zbMATH DE number 923571