FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4386297788> ?p ?o ?g. }

• W4386297788 endingPage "221" @default.
• W4386297788 startingPage "206" @default.
• W4386297788 abstract "Solving a sparse linear system of the form $$Ax=b$$ is a common engineering task, e.g., as a step in approximating solutions of differential equations. Inverting a large matrix A is often too expensive, and instead engineers rely on iterative methods, which progressively approximate the solution x of the linear system in several iterations, where each iteration is a much less expensive (sparse) matrix-vector multiplication. We present a formal proof in the Coq proof assistant of the correctness, accuracy and convergence of one prominent iterative method, the Jacobi iteration. The accuracy and convergence properties of Jacobi iteration are well-studied, but most past analyses were performed in real arithmetic; instead, we study those properties, and prove our results, in floating-point arithmetic. We then show that our results are properly reflected in a concrete implementation in the C language. Finally, we show that the iteration will not overflow, under assumptions that we make explicit. Notably, our proofs are faithful to the details of the implementation, including C program semantics and floating-point arithmetic." @default.
• W4386297788 created "2023-08-31" @default.
• W4386297788 creator A5002069299 @default.
• W4386297788 creator A5004766305 @default.
• W4386297788 creator A5059845097 @default.
• W4386297788 creator A5070988471 @default.
• W4386297788 creator A5073697071 @default.
• W4386297788 date "2023-01-01" @default.
• W4386297788 modified "2023-09-27" @default.
• W4386297788 title "Verified Correctness, Accuracy, and Convergence of a Stationary Iterative Linear Solver: Jacobi Method" @default.
• W4386297788 cites W1486558830 @default.
• W4386297788 cites W1500709119 @default.
• W4386297788 cites W1506342804 @default.
• W4386297788 cites W1575701986 @default.
• W4386297788 cites W1975906542 @default.
• W4386297788 cites W2020804487 @default.
• W4386297788 cites W2026417691 @default.
• W4386297788 cites W2042228793 @default.
• W4386297788 cites W2047163458 @default.
• W4386297788 cites W2130920933 @default.
• W4386297788 cites W2147177731 @default.
• W4386297788 cites W2792757320 @default.
• W4386297788 cites W2793741686 @default.
• W4386297788 cites W2964164193 @default.
• W4386297788 cites W3099251155 @default.
• W4386297788 cites W3138238758 @default.
• W4386297788 cites W3177469998 @default.
• W4386297788 cites W4221149319 @default.
• W4386297788 cites W4312663372 @default.
• W4386297788 cites W4320062178 @default.
• W4386297788 cites W56092462 @default.
• W4386297788 doi "https://doi.org/10.1007/978-3-031-42753-4_14" @default.
• W4386297788 hasPublicationYear "2023" @default.
• W4386297788 type Work @default.
• W4386297788 citedByCount "0" @default.
• W4386297788 crossrefType "book-chapter" @default.
• W4386297788 hasAuthorship W4386297788A5002069299 @default.
• W4386297788 hasAuthorship W4386297788A5004766305 @default.
• W4386297788 hasAuthorship W4386297788A5059845097 @default.
• W4386297788 hasAuthorship W4386297788A5070988471 @default.
• W4386297788 hasAuthorship W4386297788A5073697071 @default.
• W4386297788 hasConcept C106487976 @default.
• W4386297788 hasConcept C108710211 @default.
• W4386297788 hasConcept C11413529 @default.
• W4386297788 hasConcept C114614502 @default.
• W4386297788 hasConcept C134306372 @default.
• W4386297788 hasConcept C159694833 @default.
• W4386297788 hasConcept C159985019 @default.
• W4386297788 hasConcept C162324750 @default.
• W4386297788 hasConcept C192562407 @default.
• W4386297788 hasConcept C199360897 @default.
• W4386297788 hasConcept C2524010 @default.
• W4386297788 hasConcept C2777303404 @default.
• W4386297788 hasConcept C2778770139 @default.
• W4386297788 hasConcept C2780595030 @default.
• W4386297788 hasConcept C28826006 @default.
• W4386297788 hasConcept C33923547 @default.
• W4386297788 hasConcept C41008148 @default.
• W4386297788 hasConcept C50522688 @default.
• W4386297788 hasConcept C55439883 @default.
• W4386297788 hasConcept C67923128 @default.
• W4386297788 hasConcept C6802819 @default.
• W4386297788 hasConcept C94523830 @default.
• W4386297788 hasConceptScore W4386297788C106487976 @default.
• W4386297788 hasConceptScore W4386297788C108710211 @default.
• W4386297788 hasConceptScore W4386297788C11413529 @default.
• W4386297788 hasConceptScore W4386297788C114614502 @default.
• W4386297788 hasConceptScore W4386297788C134306372 @default.
• W4386297788 hasConceptScore W4386297788C159694833 @default.
• W4386297788 hasConceptScore W4386297788C159985019 @default.
• W4386297788 hasConceptScore W4386297788C162324750 @default.
• W4386297788 hasConceptScore W4386297788C192562407 @default.
• W4386297788 hasConceptScore W4386297788C199360897 @default.
• W4386297788 hasConceptScore W4386297788C2524010 @default.
• W4386297788 hasConceptScore W4386297788C2777303404 @default.
• W4386297788 hasConceptScore W4386297788C2778770139 @default.
• W4386297788 hasConceptScore W4386297788C2780595030 @default.
• W4386297788 hasConceptScore W4386297788C28826006 @default.
• W4386297788 hasConceptScore W4386297788C33923547 @default.
• W4386297788 hasConceptScore W4386297788C41008148 @default.
• W4386297788 hasConceptScore W4386297788C50522688 @default.
• W4386297788 hasConceptScore W4386297788C55439883 @default.
• W4386297788 hasConceptScore W4386297788C67923128 @default.
• W4386297788 hasConceptScore W4386297788C6802819 @default.
• W4386297788 hasConceptScore W4386297788C94523830 @default.
• W4386297788 hasLocation W43862977881 @default.
• W4386297788 hasOpenAccess W4386297788 @default.
• W4386297788 hasPrimaryLocation W43862977881 @default.
• W4386297788 hasRelatedWork W1503006265 @default.
• W4386297788 hasRelatedWork W1559922524 @default.
• W4386297788 hasRelatedWork W1834710643 @default.
• W4386297788 hasRelatedWork W2011497114 @default.
• W4386297788 hasRelatedWork W2074512878 @default.
• W4386297788 hasRelatedWork W2348350842 @default.
• W4386297788 hasRelatedWork W3040758895 @default.
• W4386297788 hasRelatedWork W3184983074 @default.
• W4386297788 hasRelatedWork W4200634329 @default.
• W4386297788 hasRelatedWork W2889431757 @default.

• next