On Chebyshev Polynomials of Matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00346245" target="_blank" >RIV/67985807:_____/10:00346245 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On Chebyshev Polynomials of Matrices
Original language description
The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial ofA. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well-known properties of Chebyshev polynomials of compact sets in the complex plane. We also derive explicit formulas of the Chebyshev polynomials of certain classes of matrices, and explore the relation between Chebyshev polynomials of one of these matrix classes and Chebyshev polynomials of lemniscatic regions in the complex plane.
Czech name
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Czech description
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Project
<a href="/en/project/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP) Z - Vyzkumny zamer (s odkazem do CEZ) I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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