On Abel-Hermite-Birkhoff Interpolation
Abhinav Sharma, J. Prasad · SIAM Journal on Numerical Analysis · 1968
Previous article Next article On Abel-Hermite-Birkhoff InterpolationA. Sharma and J. PrasadA. Sharma and J. Prasadhttps://doi.org/10.1137/0705062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] George David Birkhoff, General mean value and remainder theorems with applications to mechanical differentiation and quadrature, Trans. Amer. Math. Soc., 7 (1906), 107–136 MR1500736 37.0308.02 CrossrefGoogle Scholar[2] P. M. Hummel and , C. L. Seebeck, Jr., A generalization of Taylor's expansion, Amer. Math. Monthly, 56 (1949), 243–247 MR0028907 0037.17601 CrossrefGoogle Scholar[3] A. B. Nemeth, Interpolating polynomials of type $0,n,2n,\cdots,kn$, Math. Reviews, 32 (1966), #1488, Abstract Google Scholar[4] N. Obreschkoff, Neue Quadraturformeln, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl., 1940 (1940), 20– MR0003867 0024.02602 Google Scholar[5] G. Pólya, Bermerkungen zur Interpolation und zur Näherungstheorie der Balkenbiegung, Z. Angew. Math. Mech., 11 (1931), 445–449 0003.27302 CrossrefGoogle Scholar[6] Hillel Poritsky, On certain polynomial and other approximations to analytic functions, Trans. Amer. Math. Soc., 34 (1932), 274–331 MR1501639 0004.34307 CrossrefGoogle Scholar[7] I. J. Schoenberg, On Hermite-Birkhoff interpolation, J. Math. Anal. Appl., 16 (1966), 538–543 10.1016/0022-247X(66)90160-0 MR0203307 0156.28702 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Numerical strategies of computing the luminosity distance21 January 2011 | Monthly Notices of the Royal Astronomical Society, Vol. 412, No. 4 Cross Ref An error term and uniqueness for Hermite–Birkhoff interpolation involving only function values and/or first derivative valuesJournal of Computational and Applied Mathematics, Vol. 212, No. 1 Cross Ref On Hermite-Birkhoff interpolationJournal of Approximation Theory, Vol. 6, No. 1 Cross Ref Some Poised and Nonpoised Problems of InterpolationA. Sharma18 July 2006 | SIAM Review, Vol. 14, No. 1AbstractPDF (2161 KB)Birkhoff InterpolationG. G. Lorentz and K. L. Zeller14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 8, No. 1AbstractPDF (539 KB)Solving confluent Vandermonde systems of Hermite typeNumerische Mathematik, Vol. 18, No. 1 Cross Ref Interpolation in the Solution Sets of Ordinary Differential EquationsRonald M. Mathsen17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 1, No. 1AbstractPDF (827 KB)A Partial Characterization of Poised Hermite–Birkhoff Interpolation ProblemsK. Atkinson and A. Sharma14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 6, No. 2AbstractPDF (443 KB) Volume 5, Issue 4| 1968SIAM Journal on Numerical Analysis History Submitted:27 November 1967Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705062Article page range:pp. 864-881ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics