Least Squares Fitting of Polynomials to Irregularly Spaced Data

Abstract

Next article Least Squares Fitting of Polynomials to Irregularly Spaced DataA. T. BerztissA. T. Berztisshttps://doi.org/10.1137/1006059PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. A. Fisher, Studies in crop variation. I. An examination of the yield of dressed grain from Broadbalk, J. Agricult. Sci., 11 (1921), 107–135 CrossrefGoogle Scholar[2] Raymond T. Birge, Least-squares' fitting of data by means of polynomials. Mathematical appendix by J. W. Weinberg, Rev. Modern Physics, 19 (1947), 298–360 10.1103/RevModPhys.19.298 MR0024683 CrossrefGoogle Scholar[3] P. G. Guest, Numerical methods of curve fitting, Cambridge University Press, New York, 1961xiv+422 MR0120762 0097.13905 Google Scholar[4] R. A. Fisher and , F. Yates, Statistical Tables for Biological, Agricultural and Medical Research, Oliver and Boyd, Edinburgh-London, 1957 0079.35206 Google Scholar[5] R. W. Hamming, Numerical methods for scientists and engineers, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York, 1962xvii+411, San Francisco-Toronto-London MR0137279 0952.65500 Google Scholar[6] George E. P. Box, Fitting empirical data, Ann. New York Acad. Sci., 86 (1960), 792–816 (1960) MR0116431 0104.13202 ISIGoogle Scholar[7] M. A. Efroymson, A. Ralston and , H. S. Wilf, Multiple regression analysisMathematical methods for digital computers, Wiley, New York, 1960, 191–203 MR0117923 Google Scholar[8] Eduard L. Stiefel, Numerical methods of Tchebycheff approximation, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, 217–232 MR0107961 0083.35502 Google Scholar[9] A. M. Turing, Rounding-off errors in matrix processes, Quart. J. Mech. Appl. Math., 1 (1948), 287–308 MR0028100 0033.28501 CrossrefISIGoogle Scholar[10] C. Lanczos, Applied Analysis, Pitman, London, 1957 Google Scholar[11] P. G. Guest, Orthogonal polynomials in the least squares fitting of observations, Philos. Mag. (7), 41 (1950), 124–137 MR0035110 0036.36503 CrossrefGoogle Scholar[12] J. G. Hayes and , T. Vickers, The fitting of polynomials to unequally-spaced data, Philos. Mag. (7), 42 (1951), 1387–1400 MR0048159 0045.21903 CrossrefISIGoogle Scholar[13] S. Rushton, On least squares fitting by orthonormal polynomials using the Choleski method, J. Roy. Statist. Soc. Ser. B., 13 (1951), 92–99 MR0048157 0043.33604 Google Scholar[14] John Wishart and , Theocharis Metakides, Orthogonal polynomial fitting, Biometrika, 40 (1953), 361–369 MR0059062 0052.35603 CrossrefISIGoogle Scholar[15] J. H. Wilkinson, Error analysis of direct methods of matrix inversion, J. Assoc. Comput. Mach., 8 (1961), 281–330 MR0176602 0109.09005 CrossrefGoogle Scholar[16] Alston S. Householder, Principles of numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953, 221– MR0059056 0051.34602 Google Scholar[17] Eduard L. Stiefel, Kernel polynomials in linear algebra and their numerical applications, Nat. Bur. Standards Appl. Math. Ser., 1958 (1958), 1–22, U.S. Govt. Printing Office, 1958. (An earlier (1955) multilithed report is quoted in Ref. [19]) MR0092214 0171.35703 Google Scholar[18] C. Lanczos, Spectroscopic eigenvalue analysis, J. Washington Acad. Sci., 45 (1955), 315–323, See also Ref. [10], p. 374 MR0074934 Google Scholar[19] George E. Forsythe, Generation and use of orthogonal polynomials for data-fitting with a digital computer, J. Soc. Indust. Appl. Math., 5 (1957), 74–88 10.1137/0105007 MR0092208 0083.35503 LinkISIGoogle Scholar[20] Marcia Ascher and , George E. Forsythe, SWAC experiments on the use of orthogonal polynomials for data fitting, J. Assoc. Comput. Mach., 5 (1958), 9–21 MR0093011 0090.34705 CrossrefISIGoogle Scholar[21] D. S. Robson, A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced, Biometrics, 15 (1959), 187–191 MR0103573 0085.13711 CrossrefISIGoogle Scholar[22] Philip J. Davis and , Philip Rabinowitz, Advances in orthonormalizing computationAdvances in Computers, Vol. 2, Academic Press, New York, 1961, 55–133, London MR0138189 0136.13405 CrossrefGoogle Scholar[23] Jack Laderman, The square root method for solving simultaneous linear equations, Math. Tables and Other Aids to Computation, 3 (1948), 13–16 MR0025263 CrossrefGoogle Scholar[24] C. W. Clenshaw, Curve fitting with a digital computer, Comput. J., 2 (1959/1960), 170–173 10.1093/comjnl/2.4.170 MR0109429 0095.11801 CrossrefISIGoogle Scholar[25] C. W. Clenshaw, A note on the summation of Chebyshev series, Math. Tables Aids Comput., 9 (1955), 118–120 MR0071856 0065.05403 CrossrefGoogle Scholar[26] D. W. Martin, Polynomial representation of some ship section area curves and the calculation of the associated wave resistance, Quart. J. Mech. Appl. Math., 14 (1961), 49–58 MR0119393 0099.21703 CrossrefISIGoogle Scholar[27] A. D. Booth, Numerical Methods, Butterworths Scientific Publications, London, 1957, 43– 0077.32203 Google Scholar[28] A. Michels, , J. C. Abels, , C. A. Ten Seldam and , W. De Graaff, Polynomial representation of experimental data; application to virial coefficients of gases, Physica, 26 (1960), 381–392 10.1016/0031-8914(60)90028-8 CrossrefISIGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Photogrammetrische Auswertung digitaler Bilder – Neue Methoden der Kamerakalibration, dichten Bildzuordnung und Interpretation von PunktwolkenPhotogrammetrie und Fernerkundung | 4 March 2017 Cross Ref Photogrammetrische Auswertung digitaler Bilder – Neue Methoden der Kamerakalibration, dichten Bildzuordnung und Interpretation von PunktwolkenHandbuch der Geodäsie | 24 February 2016 Cross Ref A Flexible Mathematical Method for Camera Calibration in Digital Aerial PhotogrammetryPhotogrammetric Engineering & Remote Sensing, Vol. 78, No. 10 | 21 October 2013 Cross Ref Vibrational energy levels for symmetric and asymmetric isotopomers of ammonia with an exact kinetic energy operator and new potential energy surfacesThe Journal of Chemical Physics, Vol. 118, No. 14 | 8 Apr 2003 Cross Ref Fitting polynomials to main effects in multi factor experiments: unequal spacing and unbalanced data with no missing cellsCommunications in Statistics - Theory and Methods, Vol. 28, No. 12 | 1 Jan 1999 Cross Ref Rejecting outliers and estimating errors in an orthogonal-regression frameworkPhilosophical Transactions of the Royal Society of London. 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