Previous article Error Bounds for Some Chebyshev Methods of Approximation and IntegrationChristopher T. H. Baker and Pauline A. RadcliffeChristopher T. H. Baker and Pauline A. Radcliffehttps://doi.org/10.1137/0707023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe discuss the application of Peano theory, Lebesgue functions, and the theory of best polynomial approximation to the determination of a priori bounds on the error in some Chebyshev methods.[1] G. Alexits, Convergence problems of orthogonal series, Translated from the German by I. Földer. International Series of Monographs in Pure and Applied Mathematics, Vol. 20, Pergamon Press, New York, 1961ix+350 MR0218827 0098.27403 Google Scholar[2] Christopher T. H. Baker, On the nature of certain quadrature formulas and their errors, SIAM J. Numer. Anal., 5 (1968), 783–804 10.1137/0705059 MR0245200 0216.23101 LinkISIGoogle Scholar[3] Christopher T. H. Baker, The error in polynomial interpolation, Numer. Math., 15 (1970), 315–319 10.1007/BF02165122 MR0281314 0187.10503 CrossrefISIGoogle Scholar[4] M. M. Chawla, Error estimates for the Clenshaw-Curtis quadrature, Math. Comp., 22 (1968), 651–656 MR0228169 0162.47801 CrossrefISIGoogle Scholar[5] E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York, 1966xii+259 MR0222517 0161.25202 Google Scholar[6] C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty's Stationery Office, London, 1962iv+36 MR0142793 0114.07101 Google Scholar[7] P. J. Davis, Interpolation and approximation, Blasidell, new york, 1965 Google Scholar[8] L. Fox and , I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London, 1968ix+205, Oxford Mathematical Handbooks MR0228149 Google Scholar[9] W. Fraser and , M. W. Wilson, Remarks on the Clenshaw-Curtis quadrature scheme, SIAM Rev., 8 (1966), 322–327 10.1137/1008064 MR0203937 0173.18604 LinkISIGoogle Scholar[10] M. Golomb, Lectures on theory of approximation, Applied Mathematics Division, Argonne National Laboratory, Argonne, lll, 1962 Google Scholar[11] J. P. Imhof, On the method for numerical integration of Clenshaw and Curtis, Numer. Math., 5 (1963), 138–141 10.1007/BF01385885 MR0157482 0115.11702 CrossrefGoogle Scholar[12] C. Lanczos, Tables of Chebyshev polynomials Sn(x) and Cn(x), National Bureau of Standards Applied Mathematics Series, No. 9, U. S. Government Printing Office, Washington, D. C., 1952xxx+161 MR0068893 0049.21201 Google Scholar[13] D. C. Lewis, Polynomial least square approximations, Amer. J. Math., 69 (1947), 273–278 MR0020670 0033.35603 CrossrefISIGoogle Scholar[14] M. J. D. Powell, On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria, Comput. J., 9 (1967), 404–407 MR0208807 0147.14305 CrossrefISIGoogle Scholar[15] P. A. Radcliffe, Masters Thesis, Error bounds for Chebyshev approximants, Master's thesis, University of Manchester, England, 1968 Google Scholar[16] A. H. Stroud and , Don Secrest, Gaussian quadrature formulas, Prentice-Hall Inc., Englewood Cliffs, N.J., 1966ix+374 MR0202312 0156.17002 Google Scholar Previous article FiguresRelatedReferencesCited ByDetails A simple technique for calculation of numerical integration errors for physically meaningful functionsAfrika Matematika, Vol. 25, No. 1 | 10 August 2012 Cross Ref Some polynomial projections with finite carrierJournal of Approximation Theory, Vol. 34, No. 3 | 1 Mar 1982 Cross Ref Volume 7, Issue 2| 1970SIAM Journal on Numerical Analysis199-327 History Submitted:13 May 1969Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707023Article page range:pp. 317-327ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics