FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2892361963> ?p ?o ?g. }

• W2892361963 abstract "The approximation of a multiple isolated root is a difficult problem. In fact the root can even be a repulsive root for a fixed point method like the Newton method. However there exists a huge literature on this topic but the answers given are not satisfactory. Numerical methods allowing a local convergence analysis work often under specific hypotheses. This viewpoint favouring numerical analysis forgets the geometry and the structure of the local algebra. Thus appeared so-called symbolic-numeric methods, yet full of lessons, but their precise numerical analysis is still missing. We propose in this paper a method of symbolic-numeric kind, whose numerical treatment is certified. The general idea is to construct a finite sequence of systems, admitting the same root, and called the deflation sequence, so that the multiplicity of the root drops strictly between two successive systems. So the root becomes regular. Then we can extract a regular square system we call deflated system. We described already the construction of this deflated sequence when the singular root is known. The originality of this paper consists on one hand to construct a deflation sequence from a point close to the root and on the other hand to give a numerical analysis of this method. Analytic square integrable functions build the functional frame. Using the Bergman kernel, reproducing kernel of this functional frame, we are able to give a $alpha$-theory {a} la Smale. Furthermore we present new results on the determination of the numerical rank of a matrix and the closeness to zero of the evaluation map. As an important consequence we give an algorithm computing a deflation sequence free of $epsilon$, threshold quantity measuring the numerical approximation, meaning that the entry of this algorithm does not involve the variable $epsilon$." @default.
• W2892361963 created "2018-09-27" @default.
• W2892361963 creator A5014710360 @default.
• W2892361963 creator A5026805734 @default.
• W2892361963 date "2018-09-14" @default.
• W2892361963 modified "2023-09-25" @default.
• W2892361963 title "Approximation Num'erique de Racines Isol'ees Multiples de Syst`emes Analytiques" @default.
• W2892361963 cites W1550331971 @default.
• W2892361963 cites W1970136394 @default.
• W2892361963 cites W1972632202 @default.
• W2892361963 cites W1977307928 @default.
• W2892361963 cites W1984396462 @default.
• W2892361963 cites W1985790586 @default.
• W2892361963 cites W1988398326 @default.
• W2892361963 cites W1988646993 @default.
• W2892361963 cites W1996711162 @default.
• W2892361963 cites W2004026774 @default.
• W2892361963 cites W2005164796 @default.
• W2892361963 cites W2009126887 @default.
• W2892361963 cites W2015721832 @default.
• W2892361963 cites W2017478419 @default.
• W2892361963 cites W2022825799 @default.
• W2892361963 cites W2032671060 @default.
• W2892361963 cites W2033536176 @default.
• W2892361963 cites W2033936708 @default.
• W2892361963 cites W2035078157 @default.
• W2892361963 cites W2036702455 @default.
• W2892361963 cites W2040076922 @default.
• W2892361963 cites W2041176477 @default.
• W2892361963 cites W2043938310 @default.
• W2892361963 cites W2053738112 @default.
• W2892361963 cites W2064980127 @default.
• W2892361963 cites W2071860648 @default.
• W2892361963 cites W2073664445 @default.
• W2892361963 cites W2075776392 @default.
• W2892361963 cites W2087901668 @default.
• W2892361963 cites W2091853326 @default.
• W2892361963 cites W2101413883 @default.
• W2892361963 cites W2138412295 @default.
• W2892361963 cites W2166430540 @default.
• W2892361963 cites W2226070740 @default.
• W2892361963 cites W2283215057 @default.
• W2892361963 cites W564475342 @default.
• W2892361963 cites W571249777 @default.
• W2892361963 cites W653924242 @default.
• W2892361963 cites W658559791 @default.
• W2892361963 hasPublicationYear "2018" @default.
• W2892361963 type Work @default.
• W2892361963 sameAs 2892361963 @default.
• W2892361963 citedByCount "0" @default.
• W2892361963 crossrefType "posted-content" @default.
• W2892361963 hasAuthorship W2892361963A5014710360 @default.
• W2892361963 hasAuthorship W2892361963A5026805734 @default.
• W2892361963 hasConcept C11577676 @default.
• W2892361963 hasConcept C134306372 @default.
• W2892361963 hasConcept C138885662 @default.
• W2892361963 hasConcept C171078966 @default.
• W2892361963 hasConcept C2524010 @default.
• W2892361963 hasConcept C2778112365 @default.
• W2892361963 hasConcept C28826006 @default.
• W2892361963 hasConcept C33923547 @default.
• W2892361963 hasConcept C41895202 @default.
• W2892361963 hasConcept C48753275 @default.
• W2892361963 hasConcept C54355233 @default.
• W2892361963 hasConcept C86803240 @default.
• W2892361963 hasConceptScore W2892361963C11577676 @default.
• W2892361963 hasConceptScore W2892361963C134306372 @default.
• W2892361963 hasConceptScore W2892361963C138885662 @default.
• W2892361963 hasConceptScore W2892361963C171078966 @default.
• W2892361963 hasConceptScore W2892361963C2524010 @default.
• W2892361963 hasConceptScore W2892361963C2778112365 @default.
• W2892361963 hasConceptScore W2892361963C28826006 @default.
• W2892361963 hasConceptScore W2892361963C33923547 @default.
• W2892361963 hasConceptScore W2892361963C41895202 @default.
• W2892361963 hasConceptScore W2892361963C48753275 @default.
• W2892361963 hasConceptScore W2892361963C54355233 @default.
• W2892361963 hasConceptScore W2892361963C86803240 @default.
• W2892361963 hasLocation W28923619631 @default.
• W2892361963 hasOpenAccess W2892361963 @default.
• W2892361963 hasPrimaryLocation W28923619631 @default.
• W2892361963 isParatext "false" @default.
• W2892361963 isRetracted "false" @default.
• W2892361963 magId "2892361963" @default.
• W2892361963 workType "article" @default.