Sensitivity of solutions of linear DAE to perturbations of the system matrices

R.M.M. Mattheij; P.M.E.J. Wijckmans

doi:10.1023/A:1019158524005

Sensitivity of solutions of linear DAE to perturbations of the system matrices

R.M.M. Mattheij, P.M.E.J. Wijckmans

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

Abstract

This paper studies the effect of perturbations in the system matrices of linear Differential Algebraic Equations (DAE) onto the solutions. It turns out that these may result in a more complicated perturbation pattern for higher index problems than in the case for (standard) additive perturbations. We give an analysis here for linear index-1 and index-2 problems, which, however, has clear ramifications in nonlinear problems (e.g., via the Newton process). This analysis is sustained by a number of examples.

Original language	English
Pages (from-to)	159-171
Number of pages	13
Journal	Numerical Algorithms
Volume	19
Issue number	1-4
DOIs	https://doi.org/10.1023/A:1019158524005
Publication status	Published - 1998

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title = "Sensitivity of solutions of linear DAE to perturbations of the system matrices",

abstract = "This paper studies the effect of perturbations in the system matrices of linear Differential Algebraic Equations (DAE) onto the solutions. It turns out that these may result in a more complicated perturbation pattern for higher index problems than in the case for (standard) additive perturbations. We give an analysis here for linear index-1 and index-2 problems, which, however, has clear ramifications in nonlinear problems (e.g., via the Newton process). This analysis is sustained by a number of examples.",

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AB - This paper studies the effect of perturbations in the system matrices of linear Differential Algebraic Equations (DAE) onto the solutions. It turns out that these may result in a more complicated perturbation pattern for higher index problems than in the case for (standard) additive perturbations. We give an analysis here for linear index-1 and index-2 problems, which, however, has clear ramifications in nonlinear problems (e.g., via the Newton process). This analysis is sustained by a number of examples.

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