| Naslov: | Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding |
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| Avtorji: | ID He, Haoze (Avtor)
ID Kressner, Daniel (Avtor)
ID Plestenjak, Bor (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (3,88 MB)
MD5: E66AC2A60ACC80A7E41729BFCCAC7F73
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s11075-024-01971-0
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | It is well known that a family of $n \times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the $n$ joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to such joint eigenvalues for a family of (nearly) commuting matrices. This task arises, for example, in solvers for multiparameter eigenvalue problems and systems of multivariate polynomials, which are our main motivations. We propose and analyze a simple approach that computes eigenvalues as one-sided or two-sided Rayleigh quotients from eigenvectors of a random linear combination of the matrices in the family. We provide some analysis and numerous numerical examples, showing that such randomized approaches can compute semisimple joint eigenvalues accurately and lead to improved performance of existing solvers. |
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| Ključne besede: | commuting matrices, joint eigenvalues, Rayleigh quotient, randomized numerical linear algebra, multiparameter eigenvalue problems, polynomial systems |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.11.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | str. 861–892 |
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| Številčenje: | Vol. 100, iss. 3 |
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| PID: | 20.500.12556/DiRROS-23878  |
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| UDK: | 519.6 |
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| ISSN pri članku: | 1017-1398 |
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| DOI: | 10.1007/s11075-024-01971-0 |
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| COBISS.SI-ID: | 215046403 |
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| Opomba: |
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| Datum objave v DiRROS: | 16.10.2025 |
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| Število ogledov: | 213 |
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| Število prenosov: | 114 |
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| Metapodatki: |    |
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