Matches in SemOpenAlex for { <https://semopenalex.org/work/W2010901305> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W2010901305 endingPage "561" @default.
- W2010901305 startingPage "561" @default.
- W2010901305 abstract "Since properly normalized Chebyshev polynomials of the first kind T,(z) satisfy (Tm, Tn) = f Tm(z)Tn(z) 1i z-h112Idz1 _ 8mn for ellipses E, with foci at ?1, any function analytic in E, has an expansion,f(z) = E ajT,(z) with a. = (f, T,n). Applying the integration error operator E yields EJ =E anE(Tn). Applying the Cauchy-Schwarz inequality to E(f) leads to the inequality IE(f I1 < E lanl E IE(T.) 12 = I If I III JEJ 12. IEII can be computed for any integration rule and approximated quite accurately for Gaussian integration rules. The bound for IE(f)I using this norm is compared to that using a previously studied norm based on Chebyshev polynomials of the second kind and is shown to be superior in practical situations. Other results involving the latter norm are carried over to the new norm. 1. Davis and Rabinowitz [6], following the work of Davis [3], developed a new method for bounding the truncation error in the numerical integration of functions analytic over the interval of integration, standardized to [-1, 1]. This method was based on the fact that every such function could be continued analytically into a region enclosed by one of a family of confocal ellipses e, with foci at i 1, where p = a + b, a is the semimajor axis of Ep, and b = (a2 1)1/2 is the semiminor axis. Error coefficients o(R, p) were computed for various values of p and for several integration rules R, where n (1) R(f) 3 E wif(xi) is determined by a particular choice of weights wi and abscissas xi, i = 1, * * , n. The o(R, f) were computed using the Chebyshev polynomials of the second kind U,,(Z) which are orthogonal over the interior of ep with respect to the inner product (2) (f, g)p =f f(z)g(z) dx dy. Ep They are given explicitly by t' e formula (3) a2(R p) 4 E (k + 1)[I +(_1)k 1 UA(XJ] ( 2k+2 -2P-2 Received November 26, 1968, revised December 18, 1969. AMS Subject Classifications. Primary 6555, 6580." @default.
- W2010901305 created "2016-06-24" @default.
- W2010901305 creator A5044367398 @default.
- W2010901305 creator A5072200542 @default.
- W2010901305 date "1970-09-01" @default.
- W2010901305 modified "2023-09-26" @default.
- W2010901305 title "New error coefficients for estimating quadrature errors for analytic functions" @default.
- W2010901305 cites W2014114127 @default.
- W2010901305 cites W2025862753 @default.
- W2010901305 cites W2030579847 @default.
- W2010901305 cites W2040341368 @default.
- W2010901305 cites W2051999988 @default.
- W2010901305 cites W2073570359 @default.
- W2010901305 cites W2082115322 @default.
- W2010901305 cites W2316418224 @default.
- W2010901305 cites W2316785640 @default.
- W2010901305 cites W2334596606 @default.
- W2010901305 cites W2588992765 @default.
- W2010901305 doi "https://doi.org/10.1090/s0025-5718-1970-0275675-x" @default.
- W2010901305 hasPublicationYear "1970" @default.
- W2010901305 type Work @default.
- W2010901305 sameAs 2010901305 @default.
- W2010901305 citedByCount "20" @default.
- W2010901305 countsByYear W20109013052012 @default.
- W2010901305 countsByYear W20109013052014 @default.
- W2010901305 crossrefType "journal-article" @default.
- W2010901305 hasAuthorship W2010901305A5044367398 @default.
- W2010901305 hasAuthorship W2010901305A5072200542 @default.
- W2010901305 hasBestOaLocation W20109013051 @default.
- W2010901305 hasConcept C119599485 @default.
- W2010901305 hasConcept C127349201 @default.
- W2010901305 hasConcept C127413603 @default.
- W2010901305 hasConcept C134306372 @default.
- W2010901305 hasConcept C199343813 @default.
- W2010901305 hasConcept C205979905 @default.
- W2010901305 hasConcept C2777686260 @default.
- W2010901305 hasConcept C28826006 @default.
- W2010901305 hasConcept C33923547 @default.
- W2010901305 hasConcept C62869609 @default.
- W2010901305 hasConcept C71924100 @default.
- W2010901305 hasConceptScore W2010901305C119599485 @default.
- W2010901305 hasConceptScore W2010901305C127349201 @default.
- W2010901305 hasConceptScore W2010901305C127413603 @default.
- W2010901305 hasConceptScore W2010901305C134306372 @default.
- W2010901305 hasConceptScore W2010901305C199343813 @default.
- W2010901305 hasConceptScore W2010901305C205979905 @default.
- W2010901305 hasConceptScore W2010901305C2777686260 @default.
- W2010901305 hasConceptScore W2010901305C28826006 @default.
- W2010901305 hasConceptScore W2010901305C33923547 @default.
- W2010901305 hasConceptScore W2010901305C62869609 @default.
- W2010901305 hasConceptScore W2010901305C71924100 @default.
- W2010901305 hasIssue "111" @default.
- W2010901305 hasLocation W20109013051 @default.
- W2010901305 hasOpenAccess W2010901305 @default.
- W2010901305 hasPrimaryLocation W20109013051 @default.
- W2010901305 hasRelatedWork W1982234448 @default.
- W2010901305 hasRelatedWork W2029125963 @default.
- W2010901305 hasRelatedWork W2050278628 @default.
- W2010901305 hasRelatedWork W2064989775 @default.
- W2010901305 hasRelatedWork W2088333853 @default.
- W2010901305 hasRelatedWork W2095380571 @default.
- W2010901305 hasRelatedWork W2113978750 @default.
- W2010901305 hasRelatedWork W2180665983 @default.
- W2010901305 hasRelatedWork W2618840297 @default.
- W2010901305 hasRelatedWork W3088743119 @default.
- W2010901305 hasVolume "24" @default.
- W2010901305 isParatext "false" @default.
- W2010901305 isRetracted "false" @default.
- W2010901305 magId "2010901305" @default.
- W2010901305 workType "article" @default.