Matches in SemOpenAlex for { <https://semopenalex.org/work/W2920957510> ?p ?o ?g. }
- W2920957510 abstract "In [E. S. Gawlik, Zolotarev iterations for the matrix square root, arXiv preprint 1804.11000, (2018)], a family of iterations for computing the matrix square root was constructed by exploiting a recursion obeyed by Zolotarev's rational minimax approximants of the function $z^{1/2}$. The present paper generalizes this construction by deriving rational minimax iterations for the matrix $p^{th}$ root, where $p ge 2$ is an integer. The analysis of these iterations is considerably different from the case $p=2$, owing to the fact that when $p>2$, rational minimax approximants of the function $z^{1/p}$ do not obey a recursion. Nevertheless, we show that several of the salient features of the Zolotarev iterations for the matrix square root, including equioscillatory error, order of convergence, and stability, carry over to case $p>2$. A key role in the analysis is played by the asymptotic behavior of rational minimax approximants on short intervals. Numerical examples are presented to illustrate the predictions of the theory." @default.
- W2920957510 created "2019-03-22" @default.
- W2920957510 creator A5055428521 @default.
- W2920957510 date "2019-03-14" @default.
- W2920957510 modified "2023-10-01" @default.
- W2920957510 title "Rational Minimax Iterations for Computing the Matrix $p$th Root" @default.
- W2920957510 cites W1483804921 @default.
- W2920957510 cites W1591459231 @default.
- W2920957510 cites W1963502665 @default.
- W2920957510 cites W1981576702 @default.
- W2920957510 cites W1987255606 @default.
- W2920957510 cites W1999325142 @default.
- W2920957510 cites W1999330373 @default.
- W2920957510 cites W2001238573 @default.
- W2920957510 cites W2002292319 @default.
- W2920957510 cites W2002515088 @default.
- W2920957510 cites W2022846189 @default.
- W2920957510 cites W2033332487 @default.
- W2920957510 cites W2037881170 @default.
- W2920957510 cites W2063599529 @default.
- W2920957510 cites W2086619045 @default.
- W2920957510 cites W2094195349 @default.
- W2920957510 cites W2117547260 @default.
- W2920957510 cites W2124254976 @default.
- W2920957510 cites W2160603704 @default.
- W2920957510 cites W2275630370 @default.
- W2920957510 cites W253307310 @default.
- W2920957510 cites W2766660042 @default.
- W2920957510 cites W2798437384 @default.
- W2920957510 cites W2962822630 @default.
- W2920957510 hasPublicationYear "2019" @default.
- W2920957510 type Work @default.
- W2920957510 sameAs 2920957510 @default.
- W2920957510 citedByCount "0" @default.
- W2920957510 crossrefType "posted-content" @default.
- W2920957510 hasAuthorship W2920957510A5055428521 @default.
- W2920957510 hasConcept C10138342 @default.
- W2920957510 hasConcept C106487976 @default.
- W2920957510 hasConcept C11413529 @default.
- W2920957510 hasConcept C114614502 @default.
- W2920957510 hasConcept C11577676 @default.
- W2920957510 hasConcept C126255220 @default.
- W2920957510 hasConcept C14036430 @default.
- W2920957510 hasConcept C149728462 @default.
- W2920957510 hasConcept C159985019 @default.
- W2920957510 hasConcept C162324750 @default.
- W2920957510 hasConcept C168773036 @default.
- W2920957510 hasConcept C182306322 @default.
- W2920957510 hasConcept C192562407 @default.
- W2920957510 hasConcept C202444582 @default.
- W2920957510 hasConcept C2524010 @default.
- W2920957510 hasConcept C2777303404 @default.
- W2920957510 hasConcept C28826006 @default.
- W2920957510 hasConcept C33923547 @default.
- W2920957510 hasConcept C50522688 @default.
- W2920957510 hasConcept C75190567 @default.
- W2920957510 hasConcept C78458016 @default.
- W2920957510 hasConcept C86803240 @default.
- W2920957510 hasConceptScore W2920957510C10138342 @default.
- W2920957510 hasConceptScore W2920957510C106487976 @default.
- W2920957510 hasConceptScore W2920957510C11413529 @default.
- W2920957510 hasConceptScore W2920957510C114614502 @default.
- W2920957510 hasConceptScore W2920957510C11577676 @default.
- W2920957510 hasConceptScore W2920957510C126255220 @default.
- W2920957510 hasConceptScore W2920957510C14036430 @default.
- W2920957510 hasConceptScore W2920957510C149728462 @default.
- W2920957510 hasConceptScore W2920957510C159985019 @default.
- W2920957510 hasConceptScore W2920957510C162324750 @default.
- W2920957510 hasConceptScore W2920957510C168773036 @default.
- W2920957510 hasConceptScore W2920957510C182306322 @default.
- W2920957510 hasConceptScore W2920957510C192562407 @default.
- W2920957510 hasConceptScore W2920957510C202444582 @default.
- W2920957510 hasConceptScore W2920957510C2524010 @default.
- W2920957510 hasConceptScore W2920957510C2777303404 @default.
- W2920957510 hasConceptScore W2920957510C28826006 @default.
- W2920957510 hasConceptScore W2920957510C33923547 @default.
- W2920957510 hasConceptScore W2920957510C50522688 @default.
- W2920957510 hasConceptScore W2920957510C75190567 @default.
- W2920957510 hasConceptScore W2920957510C78458016 @default.
- W2920957510 hasConceptScore W2920957510C86803240 @default.
- W2920957510 hasLocation W29209575101 @default.
- W2920957510 hasOpenAccess W2920957510 @default.
- W2920957510 hasPrimaryLocation W29209575101 @default.
- W2920957510 hasRelatedWork W2005454998 @default.
- W2920957510 hasRelatedWork W2017240123 @default.
- W2920957510 hasRelatedWork W2025984567 @default.
- W2920957510 hasRelatedWork W2055757595 @default.
- W2920957510 hasRelatedWork W2075887887 @default.
- W2920957510 hasRelatedWork W2076483112 @default.
- W2920957510 hasRelatedWork W2077290045 @default.
- W2920957510 hasRelatedWork W2089648692 @default.
- W2920957510 hasRelatedWork W2090885779 @default.
- W2920957510 hasRelatedWork W2097541598 @default.
- W2920957510 hasRelatedWork W2151358049 @default.
- W2920957510 hasRelatedWork W2294979785 @default.
- W2920957510 hasRelatedWork W2551579815 @default.
- W2920957510 hasRelatedWork W2586863760 @default.
- W2920957510 hasRelatedWork W2596355177 @default.
- W2920957510 hasRelatedWork W2612376861 @default.
- W2920957510 hasRelatedWork W287601386 @default.