FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2113499611> ?p ?o ?g. }

• W2113499611 endingPage "687" @default.
• W2113499611 startingPage "635" @default.
• W2113499611 abstract "An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect such rapid convergence to be destroyed when carrying out computations in finite precision. The purpose of this paper is to show that this is not the case. Specifically, we show that Fourier extensions are actually numerically stable when implemented in finite arithmetic, and achieve a convergence rate that is at least superalgebraic. Thus, in this instance, ill-conditioning of the linear system does not prohibit a good approximation. In the second part of this paper we consider the issue of computing Fourier extensions from equispaced data. A result of Platte et al. (SIAM Rev. 53(2):308–318, 2011) states that no method for this problem can be both numerically stable and exponentially convergent. We explain how Fourier extensions relate to this theoretical barrier, and demonstrate that they are particularly well suited for this problem: namely, they obtain at least superalgebraic convergence in a numerically stable manner." @default.
• W2113499611 created "2016-06-24" @default.
• W2113499611 creator A5022994939 @default.
• W2113499611 creator A5065352983 @default.
• W2113499611 creator A5081964453 @default.
• W2113499611 date "2014-04-15" @default.
• W2113499611 modified "2023-10-03" @default.
• W2113499611 title "On the Numerical Stability of Fourier Extensions" @default.
• W2113499611 cites W1501601053 @default.
• W2113499611 cites W1558122728 @default.
• W2113499611 cites W1912930600 @default.
• W2113499611 cites W1964699038 @default.
• W2113499611 cites W1969313170 @default.
• W2113499611 cites W1971181547 @default.
• W2113499611 cites W2001477834 @default.
• W2113499611 cites W2011253351 @default.
• W2113499611 cites W2020044270 @default.
• W2113499611 cites W2030435498 @default.
• W2113499611 cites W2036740708 @default.
• W2113499611 cites W203940937 @default.
• W2113499611 cites W2041410208 @default.
• W2113499611 cites W2050507755 @default.
• W2113499611 cites W2052788839 @default.
• W2113499611 cites W2066313543 @default.
• W2113499611 cites W2074722757 @default.
• W2113499611 cites W2078768478 @default.
• W2113499611 cites W2080219236 @default.
• W2113499611 cites W2089171658 @default.
• W2113499611 cites W2107979779 @default.
• W2113499611 cites W2138286512 @default.
• W2113499611 cites W2161326618 @default.
• W2113499611 cites W2167208435 @default.
• W2113499611 cites W4247375400 @default.
• W2113499611 cites W4292170079 @default.
• W2113499611 cites W4320800818 @default.
• W2113499611 cites W579985084 @default.
• W2113499611 doi "https://doi.org/10.1007/s10208-013-9158-8" @default.
• W2113499611 hasPublicationYear "2014" @default.
• W2113499611 type Work @default.
• W2113499611 sameAs 2113499611 @default.
• W2113499611 citedByCount "57" @default.
• W2113499611 countsByYear W21134996112013 @default.
• W2113499611 countsByYear W21134996112014 @default.
• W2113499611 countsByYear W21134996112015 @default.
• W2113499611 countsByYear W21134996112016 @default.
• W2113499611 countsByYear W21134996112017 @default.
• W2113499611 countsByYear W21134996112018 @default.
• W2113499611 countsByYear W21134996112019 @default.
• W2113499611 countsByYear W21134996112020 @default.
• W2113499611 countsByYear W21134996112021 @default.
• W2113499611 countsByYear W21134996112022 @default.
• W2113499611 countsByYear W21134996112023 @default.
• W2113499611 crossrefType "journal-article" @default.
• W2113499611 hasAuthorship W2113499611A5022994939 @default.
• W2113499611 hasAuthorship W2113499611A5065352983 @default.
• W2113499611 hasAuthorship W2113499611A5081964453 @default.
• W2113499611 hasBestOaLocation W21134996112 @default.
• W2113499611 hasConcept C102519508 @default.
• W2113499611 hasConcept C104942944 @default.
• W2113499611 hasConcept C105795698 @default.
• W2113499611 hasConcept C106195933 @default.
• W2113499611 hasConcept C112972136 @default.
• W2113499611 hasConcept C11413529 @default.
• W2113499611 hasConcept C114614502 @default.
• W2113499611 hasConcept C119857082 @default.
• W2113499611 hasConcept C127162648 @default.
• W2113499611 hasConcept C134306372 @default.
• W2113499611 hasConcept C162324750 @default.
• W2113499611 hasConcept C175146775 @default.
• W2113499611 hasConcept C191252586 @default.
• W2113499611 hasConcept C199360897 @default.
• W2113499611 hasConcept C203024314 @default.
• W2113499611 hasConcept C207864730 @default.
• W2113499611 hasConcept C2777303404 @default.
• W2113499611 hasConcept C2778029271 @default.
• W2113499611 hasConcept C2778067643 @default.
• W2113499611 hasConcept C28826006 @default.
• W2113499611 hasConcept C31258907 @default.
• W2113499611 hasConcept C33923547 @default.
• W2113499611 hasConcept C34388435 @default.
• W2113499611 hasConcept C36503486 @default.
• W2113499611 hasConcept C41008148 @default.
• W2113499611 hasConcept C45374587 @default.
• W2113499611 hasConcept C48753275 @default.
• W2113499611 hasConcept C50522688 @default.
• W2113499611 hasConcept C57869625 @default.
• W2113499611 hasConcept C76563020 @default.
• W2113499611 hasConceptScore W2113499611C102519508 @default.
• W2113499611 hasConceptScore W2113499611C104942944 @default.
• W2113499611 hasConceptScore W2113499611C105795698 @default.
• W2113499611 hasConceptScore W2113499611C106195933 @default.
• W2113499611 hasConceptScore W2113499611C112972136 @default.
• W2113499611 hasConceptScore W2113499611C11413529 @default.
• W2113499611 hasConceptScore W2113499611C114614502 @default.
• W2113499611 hasConceptScore W2113499611C119857082 @default.
• W2113499611 hasConceptScore W2113499611C127162648 @default.
• W2113499611 hasConceptScore W2113499611C134306372 @default.
• W2113499611 hasConceptScore W2113499611C162324750 @default.

• next