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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| 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 |
| 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. |
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