FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2009185246> ?p ?o ?g. }

• W2009185246 endingPage "2285" @default.
• W2009185246 startingPage "2265" @default.
• W2009185246 abstract "In the present paper, we generalize the method suggested in an earlier paper by the author and overcome its main deficiency. First, we modify the well-known Prony method, which subsequently will be utilized for recovering exactly the locations of jump discontinuities and the associated jumps of a piecewise constant function by means of its Fourier coefficients with respect to any system of the classical orthogonal polynomials. Next, we will show that the method is applicable to a wider class of functions, namely, to the class of piecewise smooth functions—for functions which piecewise belong to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C squared left-bracket negative 1 comma 1 right-bracket> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>[</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>]</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>C^2[-1,1]</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the locations of discontinuities are approximated to within <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper O left-parenthesis 1 slash n right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>O(1/n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by means of their Fourier-Jacobi coefficients. Unlike the previous one, the generalized method is robust, since its success is independent of whether or not a location of the discontinuity coincides with a root of a classical orthogonal polynomial. In addition, the error estimate is uniform for any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-bracket c comma d right-bracket subset-of left-parenthesis negative 1 comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>[</mml:mo> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo stretchy=false>]</mml:mo> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>[c,d]subset (-1,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. To the end, we discuss the accuracy, stability, and complexity of the method and present numerical examples." @default.
• W2009185246 created "2016-06-24" @default.
• W2009185246 creator A5025461058 @default.
• W2009185246 date "2010-04-21" @default.
• W2009185246 modified "2023-10-14" @default.
• W2009185246 title "Approximation of the discontinuities of a function by its classical orthogonal polynomial Fourier coefficients" @default.
• W2009185246 cites W1132969739 @default.
• W2009185246 cites W1605419509 @default.
• W2009185246 cites W193027599 @default.
• W2009185246 cites W1989572515 @default.
• W2009185246 cites W2000496108 @default.
• W2009185246 cites W2030382489 @default.
• W2009185246 cites W2062227017 @default.
• W2009185246 cites W2071004961 @default.
• W2009185246 cites W2078114900 @default.
• W2009185246 cites W2100257039 @default.
• W2009185246 cites W2139580759 @default.
• W2009185246 cites W37489506 @default.
• W2009185246 cites W4248557058 @default.
• W2009185246 cites W4251155763 @default.
• W2009185246 cites W4252109912 @default.
• W2009185246 doi "https://doi.org/10.1090/s0025-5718-10-02366-5" @default.
• W2009185246 hasPublicationYear "2010" @default.
• W2009185246 type Work @default.
• W2009185246 sameAs 2009185246 @default.
• W2009185246 citedByCount "7" @default.
• W2009185246 countsByYear W20091852462012 @default.
• W2009185246 countsByYear W20091852462013 @default.
• W2009185246 countsByYear W20091852462015 @default.
• W2009185246 countsByYear W20091852462018 @default.
• W2009185246 countsByYear W20091852462021 @default.
• W2009185246 crossrefType "journal-article" @default.
• W2009185246 hasAuthorship W2009185246A5025461058 @default.
• W2009185246 hasBestOaLocation W20091852461 @default.
• W2009185246 hasConcept C11413529 @default.
• W2009185246 hasConcept C134306372 @default.
• W2009185246 hasConcept C15627037 @default.
• W2009185246 hasConcept C164660894 @default.
• W2009185246 hasConcept C33923547 @default.
• W2009185246 hasConcept C41008148 @default.
• W2009185246 hasConceptScore W2009185246C11413529 @default.
• W2009185246 hasConceptScore W2009185246C134306372 @default.
• W2009185246 hasConceptScore W2009185246C15627037 @default.
• W2009185246 hasConceptScore W2009185246C164660894 @default.
• W2009185246 hasConceptScore W2009185246C33923547 @default.
• W2009185246 hasConceptScore W2009185246C41008148 @default.
• W2009185246 hasIssue "272" @default.
• W2009185246 hasLocation W20091852461 @default.
• W2009185246 hasOpenAccess W2009185246 @default.
• W2009185246 hasPrimaryLocation W20091852461 @default.
• W2009185246 hasRelatedWork W1981901642 @default.
• W2009185246 hasRelatedWork W1995062154 @default.
• W2009185246 hasRelatedWork W2000496108 @default.
• W2009185246 hasRelatedWork W2046013216 @default.
• W2009185246 hasRelatedWork W2065247516 @default.
• W2009185246 hasRelatedWork W2128562764 @default.
• W2009185246 hasRelatedWork W2384102097 @default.
• W2009185246 hasRelatedWork W2953303953 @default.
• W2009185246 hasRelatedWork W3098629791 @default.
• W2009185246 hasRelatedWork W3125305985 @default.
• W2009185246 hasVolume "79" @default.
• W2009185246 isParatext "false" @default.
• W2009185246 isRetracted "false" @default.
• W2009185246 magId "2009185246" @default.
• W2009185246 workType "article" @default.