Matches in SemOpenAlex for { <https://semopenalex.org/work/W3204376350> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W3204376350 abstract "Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k in mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA. As a roadway towards gaining more understanding of convergence acceleration by AA, we study AA($m$), i.e., Anderson acceleration with finite window size $m$, applied to the case of linear fixed-point iterations $x_{k+1}=M x_{k}+b$. We write AA($m$) as a Krylov method with polynomial residual update formulas, and derive recurrence relations for the AA($m$) polynomials. Writing AA($m$) as a Krylov method immediately implies that $k$ iterations of AA($m$) cannot produce a smaller residual than $k$ iterations of GMRES without restart (but without implying anything about the relative convergence speed of (windowed) AA($m$) versus restarted GMRES($m$)). We find that the AA($m$) residual polynomials observe a periodic memory effect where increasing powers of the error iteration matrix $M$ act on the initial residual as the iteration number increases. We derive several further results based on these polynomial residual update formulas, including orthogonality relations, a lower bound on the AA(1) acceleration coefficient $beta_k$, and explicit nonlinear recursions for the AA(1) residuals and residual polynomials that do not include the acceleration coefficient $beta_k$. Using these recurrence relations we also derive new residual convergence bounds for AA(1) in the linear case, demonstrating how the per-iteration residual reduction $||r_{k+1}||/||r_{k}||$ depends strongly on the residual reduction in the previous iteration and on the angle between the prior residual vectors $r_k$ and $r_{k-1}$. We apply these results to study the influence of the initial guess on the asymptotic convergence factor of AA(1), and to study AA(1) residual convergence patterns." @default.
- W3204376350 created "2021-10-11" @default.
- W3204376350 creator A5023907914 @default.
- W3204376350 creator A5082790650 @default.
- W3204376350 date "2021-09-28" @default.
- W3204376350 modified "2023-09-23" @default.
- W3204376350 title "Anderson Acceleration as a Krylov Method with Application to Asymptotic Convergence Analysis" @default.
- W3204376350 cites W1966801132 @default.
- W3204376350 cites W1984827842 @default.
- W3204376350 cites W2038281434 @default.
- W3204376350 cites W2071486596 @default.
- W3204376350 cites W2074159967 @default.
- W3204376350 cites W2083717355 @default.
- W3204376350 cites W2100514507 @default.
- W3204376350 cites W2111507332 @default.
- W3204376350 cites W2788783617 @default.
- W3204376350 cites W2963282659 @default.
- W3204376350 cites W2964237553 @default.
- W3204376350 cites W3000824534 @default.
- W3204376350 cites W3007299075 @default.
- W3204376350 cites W3040001077 @default.
- W3204376350 cites W3124030041 @default.
- W3204376350 cites W3156003168 @default.
- W3204376350 cites W3173679549 @default.
- W3204376350 doi "https://doi.org/10.48550/arxiv.2109.14181" @default.
- W3204376350 hasPublicationYear "2021" @default.
- W3204376350 type Work @default.
- W3204376350 sameAs 3204376350 @default.
- W3204376350 citedByCount "1" @default.
- W3204376350 countsByYear W32043763502021 @default.
- W3204376350 crossrefType "posted-content" @default.
- W3204376350 hasAuthorship W3204376350A5023907914 @default.
- W3204376350 hasAuthorship W3204376350A5082790650 @default.
- W3204376350 hasBestOaLocation W32043763501 @default.
- W3204376350 hasConcept C11413529 @default.
- W3204376350 hasConcept C114614502 @default.
- W3204376350 hasConcept C117896860 @default.
- W3204376350 hasConcept C121332964 @default.
- W3204376350 hasConcept C134306372 @default.
- W3204376350 hasConcept C155332342 @default.
- W3204376350 hasConcept C155512373 @default.
- W3204376350 hasConcept C158622935 @default.
- W3204376350 hasConcept C162324750 @default.
- W3204376350 hasConcept C2777303404 @default.
- W3204376350 hasConcept C28826006 @default.
- W3204376350 hasConcept C33923547 @default.
- W3204376350 hasConcept C50522688 @default.
- W3204376350 hasConcept C62520636 @default.
- W3204376350 hasConcept C90119067 @default.
- W3204376350 hasConceptScore W3204376350C11413529 @default.
- W3204376350 hasConceptScore W3204376350C114614502 @default.
- W3204376350 hasConceptScore W3204376350C117896860 @default.
- W3204376350 hasConceptScore W3204376350C121332964 @default.
- W3204376350 hasConceptScore W3204376350C134306372 @default.
- W3204376350 hasConceptScore W3204376350C155332342 @default.
- W3204376350 hasConceptScore W3204376350C155512373 @default.
- W3204376350 hasConceptScore W3204376350C158622935 @default.
- W3204376350 hasConceptScore W3204376350C162324750 @default.
- W3204376350 hasConceptScore W3204376350C2777303404 @default.
- W3204376350 hasConceptScore W3204376350C28826006 @default.
- W3204376350 hasConceptScore W3204376350C33923547 @default.
- W3204376350 hasConceptScore W3204376350C50522688 @default.
- W3204376350 hasConceptScore W3204376350C62520636 @default.
- W3204376350 hasConceptScore W3204376350C90119067 @default.
- W3204376350 hasLocation W32043763501 @default.
- W3204376350 hasOpenAccess W3204376350 @default.
- W3204376350 hasPrimaryLocation W32043763501 @default.
- W3204376350 hasRelatedWork W1930195566 @default.
- W3204376350 hasRelatedWork W1993237915 @default.
- W3204376350 hasRelatedWork W2002097440 @default.
- W3204376350 hasRelatedWork W2358905935 @default.
- W3204376350 hasRelatedWork W2379775470 @default.
- W3204376350 hasRelatedWork W2757608559 @default.
- W3204376350 hasRelatedWork W2983559648 @default.
- W3204376350 hasRelatedWork W3134028852 @default.
- W3204376350 hasRelatedWork W3140898507 @default.
- W3204376350 hasRelatedWork W3152060313 @default.
- W3204376350 isParatext "false" @default.
- W3204376350 isRetracted "false" @default.
- W3204376350 magId "3204376350" @default.
- W3204376350 workType "article" @default.