Rational approximate solutions and error bounds for the nonsymmetric Riccati matrix differential equation
type: Item
instance of: scholarly article
title: Rational approximate solutions and error bounds for the nonsymmetric Riccati matrix differential equation
zbMATH Open document ID: 0768.65038
DOI: 10.1016/0096-3003(92)90008-O
published in: Applied Mathematics and Computation
publication date: 1992-09-27T00:00:00Z
review text: Consider the \(n \times n\) matrix Riccati differential equation \(W'(t)=C - DW(t)-W(t)A - W(t)BW(t)\), \(W(0) = W_ 0\), with constant matrix coefficients. First the interval is estimated where the exact solution is defined. Then the error of the approximate solution \(W_ q(t)\) is estimated, where \(W_ q(t)\) is obtained replacing the matrix exponential \(e^{St}\) of \(S=\bigl[{A\atop C}{B\atop -D}\bigr]\) by \(I_{2n} + St + \dots + (St)^ q/q!\).
reviewed by: V.A.Velev
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 93B50
zbMATH DE Number: 64320
zbMATH Keywords: error bounds
zbMATH Keywords: matrix Riccati differential equations
zbMATH Keywords: rational approximate solutions
zbMATH Keywords: first order system
zbMATH Keywords: matrix exponential
Wikidata QID: Q115363944
author: L. Jódar
MaRDI profile type: Publication
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full work available at URL: 0096-3003(92)90008-o
OpenAlex ID: W2080132177
description: scientific article; zbMATH DE number 64320