Regularizing algorithm for mixed matrix pencils

P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm to square complex matrices with respect to con...

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Detalles Bibliográficos
Autor: Klymchuk, Tetiana|||0000-0002-3964-6437
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/120721
Acceso en línea:https://hdl.handle.net/2117/120721
https://dx.doi.org/10.21042/AMNS.2017.1.00010
Access Level:acceso abierto
Palabra clave:Algebra
Algorithms
Matrices
Regularizing algorithm
Matrix pencils
Consimilarity
Unitary transformations
Canonical forms
Algorismes
Matrius (Matemàtica)
Àlgebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Descripción
Sumario:P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm to square complex matrices with respect to consimilarity transformations and to pairs of m-by-n complex matrices with respect to transformations $(A,B) \rightarrow (SAR; SB\bar{R})$, in which $S$ and $R$ are nonsingular matrices.