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  • Krátké rekurence pro počítání ortogonální báze Krylovova podprostoru pro danou matici A existují právě tehdy, když je adjungovaná matice k matici A polynomem v proměnné A. Ve světě iteračních metod je tento výsledek znám jako Faber-Manteuffelova věta. V tomto článku formulujeme Faber-Manteuffelova větu v řeči lineárních operátorů na konečně dimenzionálních Hilbertových prostorech a prezentujeme dva nové důkazy této věty. (cs)
  • A short recurrence for orthogonalizing Krylov subspace bases for a matrix A exists if and only if the adjoint of A is a low degree polynomial in A. In the area of iterative methods, this result is known as the Faber-Manteuffel Theorem. We here formulate this theorem in terms of linear operators on finite dimensional Hilbert spaces, and give two new proofs of the necessity part.
  • A short recurrence for orthogonalizing Krylov subspace bases for a matrix A exists if and only if the adjoint of A is a low degree polynomial in A. In the area of iterative methods, this result is known as the Faber-Manteuffel Theorem. We here formulate this theorem in terms of linear operators on finite dimensional Hilbert spaces, and give two new proofs of the necessity part. (en)
Title
  • The Faber-Manteuffel Theorem for Linear Operators
  • Faber-Manteuffelova věta pro lineární operátory (cs)
  • The Faber-Manteuffel Theorem for Linear Operators (en)
skos:prefLabel
  • The Faber-Manteuffel Theorem for Linear Operators
  • Faber-Manteuffelova věta pro lineární operátory (cs)
  • The Faber-Manteuffel Theorem for Linear Operators (en)
skos:notation
  • RIV/67985807:_____/08:00314393!RIV09-AV0-67985807
http://linked.open...avai/riv/aktivita
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  • P(1ET400300415), Z(AV0Z10300504)
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  • 3
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  • 367531
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  • RIV/67985807:_____/08:00314393
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  • cyclic subspaces; Krylov subspaces; orthogonal bases; orthogonalization; short recurrences; normal matrices (en)
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  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [E57664CB2038]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Numerical Analysis
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  • 46
http://linked.open...iv/tvurceVysledku
  • Tichý, Petr
  • Faber, V.
  • Liesen, J.
http://linked.open...ain/vavai/riv/wos
  • 000255500400011
http://linked.open...n/vavai/riv/zamer
issn
  • 0036-1429
number of pages
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