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On Singular Values Related to DAEs in Kronecker Canonical Form

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Abstract

The index and the structural properties of differential algebraic equations (DAEs) are often determined by rank considerations of the derivative array. Since the Kronecker canonical form is a well-understood standard form that permits deep insight into the properties of DAEs, in this contribution we undertake an analysis of the singular values of this specific derivative array. To this end, the special structure of the obtained block matrices is pointed out, such that some formulas for the computation and estimation of eigenvalues and singular values can be applied. Actually, we explore the relationship between the spectra of particular block tridiagonal matrices and some perturbed Jacobi matrices.

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Authors and Affiliations

  1. Beuth Hochschule für Technik Berlin, Luxemburger Str. 10, 13353, Berlin, Germany

    Diana Estévez Schwarz

  2. Department of Mathematics, Kuwait University, 13060, Safat, Kuwait

    Carlos M. da Fonseca

Authors
  1. Diana Estévez Schwarz
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  2. Carlos M. da Fonseca
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Correspondence to Diana Estévez Schwarz.

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Estévez Schwarz, D., da Fonseca, C.M. On Singular Values Related to DAEs in Kronecker Canonical Form. Mediterr. J. Math. 13, 2813–2826 (2016). https://doi.org/10.1007/s00009-015-0657-5

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  • DOI: https://doi.org/10.1007/s00009-015-0657-5

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