Zobrazeno 1 - 10
of 10
pro vyhledávání: '"D. F. Paget"'
Publikováno v:
Journal of Approximation Theory. 50:49-57
It is well known that a near minimax polynomial approximation p is obtained by truncating the Chebyshev series of a function ƒ; after n + 1 terms. It is shown that if ƒ; ϵ C (n + 1) [−1, 1], then ∥ƒ; − p ∥ may be expressed in terms of ƒ;
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::650f131e364226196a415ec6974a54e7
https://doi.org/10.1016/0021-9045(87)90065-7
https://doi.org/10.1016/0021-9045(87)90065-7
Autor:
David Elliott, D. F. Paget
Publikováno v:
BIT. 16:32-40
An algorithm, based on the use of orthogonal polynomials, for product-integration is outlined. A general discussion on the convergence of such quadrature rules for finite intervals is then given. The paper concludes with five examples for each of whi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dafc0be92880b17287d83d2ce00415ff
https://doi.org/10.1007/bf01940775
https://doi.org/10.1007/bf01940775
Autor:
D. F. Paget, David Elliott
Publikováno v:
BIT. 18:137-141
A recent theorem due to Nevai on the mean convergence of Lagrange interpolation is used to obtain sufficient conditions for the convergence of quadrature rules for product integration.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e8192616bc5c0643042e28cc6904154d
https://doi.org/10.1007/bf01931690
https://doi.org/10.1007/bf01931690
Autor:
D. F. Paget
Publikováno v:
Numerische Mathematik. 36:447-453
A quadrature rule is described for the numerical evaluation of Hadamard finite-part integrals with a double pole singularity within the range of integration. The rule is based upon the observation that such an integral is the derivative of a Cauchy p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51ef6bfc704db7035f95eef5dbbc8aba
https://doi.org/10.1007/bf01395957
https://doi.org/10.1007/bf01395957
Autor:
D. F. Paget
Publikováno v:
Journal of Approximation Theory. 50:58-68
Let s n denote the formal expansion of a function ƒ in a Jacobi series truncated after n + 1 terms. For ƒ ϵ C n + 1 [−1, 1] the uniform norm of ƒ − s n is expressed in terms of the ( n + 1)th derivative of ƒ. This expression is precise when
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b1c1d6b9431e89eb2d004a4e7cd9569
https://doi.org/10.1016/0021-9045(87)90066-9
https://doi.org/10.1016/0021-9045(87)90066-9
Autor:
D. F. Paget
Publikováno v:
BIT. 21:212-220
A quadrature rule is described for evaluating finite-part (f.p.) integrals of the form\( = \smallint _0^1 y^{ - af} (y)dy\), witha ≧ 1. The rule is obtained by interpolating tof by a polynomial which coincides withf at the shifted zeros of a Legend
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba85e2d0c66ca1dffe8e66d8c7e240c2
https://doi.org/10.1007/bf01933166
https://doi.org/10.1007/bf01933166
Autor:
David Elliott, D. F. Paget
Publikováno v:
Mathematics of Computation. 33:301-309
Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is gi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aa1bf08e5168f03e6799d3714c132005
https://doi.org/10.1090/s0025-5718-1979-0514825-2
https://doi.org/10.1090/s0025-5718-1979-0514825-2
Autor:
David Elliott, D. F. Paget
Publikováno v:
Numerische Mathematik. 19:373-385
An algorithm is described for numerically evaluating Cauchy principal value (c.p.v.) integrals of the type[Figure not available: see fulltext.]. The remainder is expressed as a contour integral, from which realistic asymptotic estimates are obtained.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6dc1bbd4fb27d53c19ca9269057893f5
https://doi.org/10.1007/bf01404920
https://doi.org/10.1007/bf01404920
Autor:
David Elliott, D. F. Paget
Publikováno v:
Numerische Mathematik. 25:287-289
In a previous paper the authors proved that a quadrature rule for Cauchy principal value integrals converged for functions satisfying a Holder condition of order one. This result is now extended to demonstrate convergence of the rule for Holder conti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0d7267ae3f58b0d144e2233a544af300
https://doi.org/10.1007/bf01399417
https://doi.org/10.1007/bf01399417
Autor:
Herta T. Freitag, H. L. Krall, Robert S. Doran, Michael Goldberg, J. A. H. Hunter, T. J. Kaczynski, W. J. Blundon, Haig Boligian, Richard L. Breisch, Ellis W. Detwiler, Gerald C. Dodds, M. G. Greening, Shiv Kumar, John Oman, D. F. Paget, Kim R. Penrose, Simeon Reich, Phil Tracy, C. s. Venkataraman, Michael Yoder, C. Stanley Ogilvy, Charles W. Trigg, G. L. N. Rao, Miss Nirmal, Huseyin Demir, E. F. Schmeichel, J. F. Rigby, Murray S. Klamkin, Sidney Spital, Hugh M. Edgar, Harley Flanders, Cecil G. Phipps, Albert Wilansky, Loring Tu, Warren Page, Norman Schaumberger, C. S. Venkataraman, Erwin Just, A. K. Austin, Francis Siwiec, Gregory Wulczyn, Hwa S. Hahn, David L. Silverman, Harold B. Curtis, E. F. Pinzka, Patricia La Fratta
Publikováno v:
Mathematics Magazine. 44:40
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::03dc4e1c56d50ec50b5e8449a40a0bf7
https://doi.org/10.2307/2688865
https://doi.org/10.2307/2688865