Matches in SemOpenAlex for { <https://semopenalex.org/work/W2077435672> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2077435672 endingPage "653" @default.
- W2077435672 startingPage "638" @default.
- W2077435672 abstract "The Toeplitz matrix $T_n$ with generating function $f ( omega ) = |1 - e ^{-i omega}|^{-2d} h( omega )$, where $d in (-frac{1}{2}, frac{1}{2})setminus {0}$ and $h(omega)$ is positive, continuous on $[-pi,pi]$, and differentiable on $[-pi,pi]setminus{0}$, has a Fisher--Hartwig singularity [M. E. Fisher and R. E. Hartwig (1968), Adv. Chem. Phys., 32, pp. 190--225]. The complexity of the preconditioned conjugate gradient (PCG) algorithm is known [R. H. Chan and M. Ng (1996), SIAM Rev., 38, pp. 427--482] to be $O(nlog n)$ for Toeplitz systems when $d = 0$. However, the effect on the PCG algorithm of the Fisher--Hartwig singularity in $T_n$ has not been explored in the literature. We show that the complexity of the conjugate gradient (CG) algorithm for solving $T_n x=b$ without any preconditioning grows asymptotically as $n^{1+|d|}log (n)$. With T. Chan's optimal circulant preconditioner $C_n$ [T. Chan (1988), SIAM J. Sci. Statist. Comput., 9, pp. 766--771], the complexity of the PCG algorithm is $O(nlog^3(n))$." @default.
- W2077435672 created "2016-06-24" @default.
- W2077435672 creator A5043896769 @default.
- W2077435672 creator A5051977708 @default.
- W2077435672 date "2005-01-01" @default.
- W2077435672 modified "2023-09-24" @default.
- W2077435672 title "On the Complexity of the Preconditioned Conjugate Gradient Algorithm for Solving Toeplitz Systems with a Fisher--Hartwig Singularity" @default.
- W2077435672 cites W1493981498 @default.
- W2077435672 cites W1533471646 @default.
- W2077435672 cites W1550150926 @default.
- W2077435672 cites W1572130374 @default.
- W2077435672 cites W1983262914 @default.
- W2077435672 cites W1988078417 @default.
- W2077435672 cites W1991469062 @default.
- W2077435672 cites W1994176509 @default.
- W2077435672 cites W2005041367 @default.
- W2077435672 cites W2015947314 @default.
- W2077435672 cites W2026406497 @default.
- W2077435672 cites W2034161641 @default.
- W2077435672 cites W2036423589 @default.
- W2077435672 cites W2043390776 @default.
- W2077435672 cites W2045351867 @default.
- W2077435672 cites W2064616889 @default.
- W2077435672 cites W2080097309 @default.
- W2077435672 cites W2084730628 @default.
- W2077435672 cites W2086989241 @default.
- W2077435672 cites W2089851716 @default.
- W2077435672 cites W2100420930 @default.
- W2077435672 cites W2138152282 @default.
- W2077435672 cites W2140971281 @default.
- W2077435672 cites W2326028551 @default.
- W2077435672 cites W2326591006 @default.
- W2077435672 cites W2332453137 @default.
- W2077435672 cites W2393675882 @default.
- W2077435672 cites W2610857016 @default.
- W2077435672 cites W2995875879 @default.
- W2077435672 cites W3013430759 @default.
- W2077435672 doi "https://doi.org/10.1137/040612117" @default.
- W2077435672 hasPublicationYear "2005" @default.
- W2077435672 type Work @default.
- W2077435672 sameAs 2077435672 @default.
- W2077435672 citedByCount "12" @default.
- W2077435672 countsByYear W20774356722013 @default.
- W2077435672 countsByYear W20774356722014 @default.
- W2077435672 crossrefType "journal-article" @default.
- W2077435672 hasAuthorship W2077435672A5043896769 @default.
- W2077435672 hasAuthorship W2077435672A5051977708 @default.
- W2077435672 hasConcept C11413529 @default.
- W2077435672 hasConcept C114614502 @default.
- W2077435672 hasConcept C115973184 @default.
- W2077435672 hasConcept C121332964 @default.
- W2077435672 hasConcept C134306372 @default.
- W2077435672 hasConcept C147710293 @default.
- W2077435672 hasConcept C159694833 @default.
- W2077435672 hasConcept C16171025 @default.
- W2077435672 hasConcept C167431342 @default.
- W2077435672 hasConcept C197336794 @default.
- W2077435672 hasConcept C202444582 @default.
- W2077435672 hasConcept C202615002 @default.
- W2077435672 hasConcept C2779557605 @default.
- W2077435672 hasConcept C33923547 @default.
- W2077435672 hasConcept C62520636 @default.
- W2077435672 hasConcept C81184566 @default.
- W2077435672 hasConceptScore W2077435672C11413529 @default.
- W2077435672 hasConceptScore W2077435672C114614502 @default.
- W2077435672 hasConceptScore W2077435672C115973184 @default.
- W2077435672 hasConceptScore W2077435672C121332964 @default.
- W2077435672 hasConceptScore W2077435672C134306372 @default.
- W2077435672 hasConceptScore W2077435672C147710293 @default.
- W2077435672 hasConceptScore W2077435672C159694833 @default.
- W2077435672 hasConceptScore W2077435672C16171025 @default.
- W2077435672 hasConceptScore W2077435672C167431342 @default.
- W2077435672 hasConceptScore W2077435672C197336794 @default.
- W2077435672 hasConceptScore W2077435672C202444582 @default.
- W2077435672 hasConceptScore W2077435672C202615002 @default.
- W2077435672 hasConceptScore W2077435672C2779557605 @default.
- W2077435672 hasConceptScore W2077435672C33923547 @default.
- W2077435672 hasConceptScore W2077435672C62520636 @default.
- W2077435672 hasConceptScore W2077435672C81184566 @default.
- W2077435672 hasIssue "3" @default.
- W2077435672 hasLocation W20774356721 @default.
- W2077435672 hasOpenAccess W2077435672 @default.
- W2077435672 hasPrimaryLocation W20774356721 @default.
- W2077435672 hasRelatedWork W2011703906 @default.
- W2077435672 hasRelatedWork W2071158387 @default.
- W2077435672 hasRelatedWork W2096176037 @default.
- W2077435672 hasRelatedWork W2125935528 @default.
- W2077435672 hasRelatedWork W2136657801 @default.
- W2077435672 hasRelatedWork W2138152282 @default.
- W2077435672 hasRelatedWork W2162069340 @default.
- W2077435672 hasRelatedWork W3190961110 @default.
- W2077435672 hasRelatedWork W2507217014 @default.
- W2077435672 hasRelatedWork W2674186696 @default.
- W2077435672 hasVolume "27" @default.
- W2077435672 isParatext "false" @default.
- W2077435672 isRetracted "false" @default.
- W2077435672 magId "2077435672" @default.
- W2077435672 workType "article" @default.