Optimal Starting Values for the Newton-Raphson Calculation of Inverses of Certain Functions

Previous article Next article Optimal Starting Values for the Newton-Raphson Calculation of Inverses of Certain FunctionsD. G. Moursund and G. D. TaylorD. G. Moursund and G. D. Taylorhttps://doi.org/10.1137/0705011PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] David G. Moursund, Chebyshev approximation using a generalized weight function, SIAM J. Numer. Anal., 3 (1966), 435–450 10.1137/0703038 MR0204936 0163.07302 LinkGoogle Scholar[2] David G. Moursund, Optimal starting values for Newton-Raphson calculation of x, Comm. ACM, 10 (1967), 430–432 10.1145/363427.363454 MR0240952 CrossrefISIGoogle Scholar[3] D. G. Moursund, Computational aspects of Chebyshev approximation using a generalized weight function, SIAM J. Numer. Anal., 5 (1968), 126–137 10.1137/0705010 MR0229366 0164.18501 LinkISIGoogle Scholar[4] John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964xi+203 MR0166520 0114.27001 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Applications of Transformation Theory: A Legacy from Zolotarev (1847–1878) Cross Ref Optimal partitioning of Newton’s method for calculating roots1 January 1980 | Mathematics of Computation, Vol. 35, No. 152 Cross Ref Numerische Methoden zur Behandlung einiger Problemklassen der nichtlinearen Tschebyscheff-Approximation mit NebenbedingungenNumerische Mathematik, Vol. 28, No. 1 Cross Ref Optimal rational starting approximationsJournal of Approximation Theory, Vol. 12, No. 2 Cross Ref Optimal starting approximations for iterative schemesJournal of Approximation Theory, Vol. 9, No. 1 Cross Ref An Improved Newton Iteration for Calculating Roots which is Optimal Cross Ref Kolmogoroff's criterion for constrained rational approximationJournal of Approximation Theory, Vol. 4, No. 2 Cross Ref Improved Newton iteration for integral roots1 January 1971 | Mathematics of Computation, Vol. 25, No. 114 Cross Ref Some Remarks on a Paper of D. G. MoursundL. Wuytack14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 7, No. 2AbstractPDF (426 KB)Optimal starting approximations for Newton's methodJournal of Approximation Theory, Vol. 3, No. 2 Cross Ref Chapter 5 The Bubnov-Galerkin Method Cross Ref Generalized logarithmic error and Newton’s method for the 𝑚th root.1 January 1970 | Mathematics of Computation, Vol. 24, No. 110 Cross Ref Uniform approximation of vector-valued functionsNumerische Mathematik, Vol. 13, No. 3 Cross Ref Nonlinear Chebychev approximation by vector-normsJournal of Approximation Theory, Vol. 2, No. 1 Cross Ref Uniform Rational Approximation Using a Generalized Weight FunctionD. G. Moursund and G. D. Taylor14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 4AbstractPDF (647 KB)Continuity of the best approximation operator for restricted range approximationsJournal of Approximation Theory, Vol. 1, No. 4 Cross Ref Uniform rational weighted approximations having restricted rangesJournal of Approximation Theory, Vol. 1, No. 4 Cross Ref On Approximation by Polynomials Having Restricted RangesG. D. Taylor3 August 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 2AbstractPDF (1067 KB)Computational Aspects of Chebyshev Approximation Using a Generalized Weight FunctionD. G. Moursund14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 1AbstractPDF (953 KB) Volume 5, Issue 1| 1968SIAM Journal on Numerical Analysis History Submitted:01 May 1967Accepted:16 September 1967Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705011Article page range:pp. 138-150ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics