Bibliography for Least Squares Polynomials

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  1. Local least squares polynomials approximations to scattered data.    
    de Tisi, F.; Feraudi, F.    
    Int. Math. J. 2 (2002), no. 1, 51--61, MathSciNet.  
  2. Generalized least-squares polynomial preconditioners for symmetric indefinite linear equations
    Liang, Y.; Weston, J.; Szularz, M.
    Parallel Computing, 2002, vol. 28, no. ER2, pp. 323-341, Ingenta.  
  3. The least squares estimates in the fuzzy polynomial prognostic models. (Chinese)  
    Zhang, Chong Gao  
    Mohu Xitong yu Shuxue 15 (2001), no. 2, 58--64, MathSciNet.  
  4. Least-Squares Polynomial Filters for Ill-Conditioned Linear Systems
    Erhel, J.; Guyomarc h, F.; Saad, Y.
    Rapport de Recherche- Institut National de Recherche en Informatique et en Automatique, 2001, no. 4175, pp. ALL, Ingenta.  
  5. Local polynomial reproduction and moving least squares approximation
    Wendland, H.
    IMA Journal of Numerical Analysis, 2001, vol. 21, no. 1, pp. 285-300, Ingenta.  
  6. Fitting Nature's Basic Functions Part I: Polynomials and Linear Least Squares
    Rust, B. W.
    Computing in Science and Engineering, 2001, vol. 3, no. 5, pp. 84-89, Ingenta.  
  7. The sensitivity of least squares polynomial approximation. Applications and computation of orthogonal polynomials
    Beckermann, Bernhard; Saff, Edward B.    
    (Oberwolfach, 1998), 1--19,  Internat. Ser. Numer. Math., 131, Birkhäuser, Basel, 1999, MathSciNet.  
  8. Least squares fitting of digital polynomial segments.  
    Zuni'c, Jovisa; Acketa, Dragan M.  
    Discrete geometry for computer imagery (Lyon, 1996), 17--23, Lecture Notes in Comput. Sci., 1176, Springer, Berlin, 1996, MathSciNet.  
  9. The development of a procedure for least squares fitting of experimental data using orthogonal polynomials. (Chinese)  
    Xi, Sheng Feng  
    J. Yiyang Teachers College 13 (1996), no. 5, 20--26, MathSciNet.  
  10. Data-Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation  
    Jianqing Fan, Irene Gijbels  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 57, No. 2. (1995), pp. 371-394., Jstor.  
  11. Lagrange and least-squares polynomials as limits of linear combinations of iterates of Bernstein and Durrmeyer polynomials.    
    Sevy, J. C.    
    J. Approx. Theory 80 (1995), no. 2, 267--271, MathSciNet.  
  12. Vector orthogonal polynomials and least squares approximation.
    Bultheel, Adhemar; Van Barel, Marc
    SIAM J. Matrix Anal. Appl. 16 (1995), no. 3, 863--885, MathSciNet.  
  13. Map-image registration accuracy using least-squares polynomials.
    Mather, P.M.
    International journal of geographical information systems, 1995, vol. 9, no. 5, pp. 543, Ingenta.  
  14. Vector Orthogonal Polynomials and Least Squares Approximation.
    Bultheel, Adhemar; Van Barel, Marc
    SIAM journal on matrix analysis and applications, 1995, vol. 16, no. 3, pp. 863, Ingenta.  
  15. Efficiency of least-squares-estimation of polynomial trend when residuals are autocorrelated.  
    Busse, Ralf; Jeske, Roland; Krämer, Walter  
    Econom. Lett. 45 (1994), no. 3, 267--271, MathSciNet.  
  16. Efficiency of Least-squares-estimation of Polynomial Trend when Residuals are Autocorrelated.
    Busse, R.; Jeske, R.; Kramer, W.
    Economics letters, 1994, vol. 45, no. 3, pp. 267, Ingenta.   
  17. Least-squares orthogonal polynomials. Computational complex analysis.  
    Brezinski, Claude; Matos, Ana C.  
    J. Comput. Appl. Math. 46 (1993), no. 1-2, 229--239, MathSciNet.  
  18. On Polynomial Gaussian Least-Squares Fits and Interpretation of the Resulting Fit-Parameters.
    Hohm, U.
    Zeitschrift fur Naturforschung. A, A journal of physical sciences, 1993, vol. 48, no. 12, pp. 878, Ingenta.  
  19. Least-squares orthogonal polynomial approximation in several independent variables.
    Caprari, R.S.
    Computers in physics, 1993, vol. 7, no. 3, pp. 336, Ingenta.  
  20. The bias of least squares polynomial interpolants.    
    Morgenthaler, S.    
    Metrika 39 (1992), no. 1, 45--55, MathSciNet.  
  21. Least-squares fitting of orthogonal polynomials to the wave-aberration function.
    Rayces, J.L.
    Applied optics, 1992, vol. 31, no. 13, pp. 2223, Ingenta.  
  22. On-Line Least-Squares Method of Estimating the Coefficients of the Orthogonal-Polynomial Expansion of a Function.
    Ranganathan, V.; Jha, A.N.; Rajamani, V.S.
    Journal of the Institution of Electronics and Telecommunication Engineers, 1991, vol. 37, no. 3, pp. 280, Ingenta.  
  23. Uniform partition and the best least-squares piecewise polynomial approximation.
    Dubeau, Francois
    Bulletin of the Australian Mathematical Society, 1991, vol. 44, no. 2, pp. 279, Ingenta.  
  24. Fast QR Decomposition of Vandermonde-Like Matrices and Polynomial Least Squares Approximation.
    Reichel, Lothar
    SIAM journal on matrix analysis and applications, 1991, vol. 12, no. 3, pp. 552, Ingenta.  
  25. Polynomial (linear in Parameters) least squares analysis when all experimental data are subject to random errors.
    Lisy, J.M.; Cholvadova, A.; Drobna, B.
    Computers & chemistry, 1991, vol. 15, no. 2, pp. 135, Ingenta.  
  26. Normal Distribution Assumption and Least Squares Estimation Function in the Model of Polynomial Regression.
    Bischoff, Wolfgang; Cremers, Heinz; Fieger, Werner
    Journal of multivariate analysis, 1991, vol. 36, no. 1, pp. 1, Ingenta.  
  27. Curve Fitting by Polynomial-Trigonometric Regression  
    R. L. Eubank, Paul Speckman  
    Biometrika, Vol. 77, No. 1. (Mar., 1990), pp. 1-9., Jstor.  
  28. Least-squares polynomial curve-fitting for calibration purposes (STATCAL-CALIBRA).
    Kragten, J.
    Analytica chimica acta, 1990, vol. 241, no. 1, pp. 1, Ingenta.  
  29. The least squares problems and orthogonal polynomials.  
    d'Almeida, Filomena; Matos, Ana Cristina; Rodrigues, Maria João  
    Orthogonal polynomials and their applications (Erice, 1990), 217--222, IMACS Ann. Comput. Appl. Math., 9, Baltzer, Basel, 1991, MathSciNet.  
  30. Least squares adaptive polynomials.  
    Passi, Ranjit M.; Morel, Claude  
    Comm. Statist. Theory Methods 18 (1989), no. 1, 315--329, MathSciNet.  
  31. Characterization of the Weights of Least Squares Adaptive Polynomials  
    Robert K. Goodrich, Ranjit M. Passi  
    SIAM Journal on Applied Mathematics, Vol. 48, No. 2. (Apr., 1988), pp. 458-464, Jstor.  
  32. Error Bounds for Least Squares Approximation by Polynomials.
    Paget, David
    Journal of approximation theory, 1988, vol. 54, no. 3, pp. 314, MathSciNet.  
  33. Piecewise Cubic Curve Fitting Algorithm  
    Zheng Yan  
    Mathematics of Computation, Vol. 49, No. 179. (Jul., 1987), pp. 203-213, Jstor.  
  34. Least Squares Polynomials in the Complex Plane and Their Use for Solving Nonsymmetric Linear Systems  
    Youcef Saad  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 1. (Feb., 1987), pp. 155-169, Jstor.  
  35. Error analysis for piecewise quadratic curve fitting algorithms.   
    DeVore, Ronald A.; Yan, Zheng   
    Comput. Aided Geom. Design 3 (1986), no. 3, 205--215, MathSciNet.  
  36. Least squares approximation by one-pass methods with piecewise polynomials.  
    Yoshimoto, F.  
    Algorithms for approximation (Shrivenham, 1985), 213--224, Inst. Math. Appl. Conf. Ser. New Ser., 10, Oxford Univ. Press, New York, 1987, MathSciNet.  
  37. Error estimates for least squares approximation by polynomials.  
    Brass, Helmut  
    J. Approx. Theory 41 (1984), no. 4, 345--349, MathSciNet.  
  38. Quadratic Pencils and Least-Squares Piecewise-Polynomial Approximation  
    Boris Mityagin  
    Mathematics of Computation, Vol. 40, No. 161. (Jan., 1983), pp. 283-300, Jstor.  
  39. Local resistance in polynomial regression and restricted least squares.  
    Polasek, W.  
    Statistics and probability (Visegrád, 1982), 283--295, Reidel, Dordrecht, 1984, MathSciNet.  
  40. The Interpretation of Least Squares Regression With Interaction or Polynomial Terms (in Notes)  
    Irwin Bernhardt, Bong S. Jung  
    The Review of Economics and Statistics, Vol. 61, No. 3. (Aug., 1979), pp. 481-483., Jstor.  
  41. Practical Curve Fitting (in Notes)  
    William Silvert  
    Limnology and Oceanography, Vol. 24, No. 4. (Jul., 1979), pp. 767-773., Jstor.  
  42. Polynomial least square interval approximation.  
    Rokne, J.  
    Computing 20 (1978), no. 2, 165--176, MathSciNet.  
  43. Polynomial least squares approximations with ill-conditioned bases.  
    Richter, G. R.; Steiger, W. L.  
    Computing 19 (1977), no. 1, 85--88, MathSciNet.  
  44. A Comparison of Two Algorithms for Absolute Deviation Curve Fitting (in Applications)  
    R. D. Armstrong, E. L. Frome  
    Journal of the American Statistical Association, Vol. 71, No. 354. (Jun., 1976), pp. 328-330., Jstor.  
  45. Curve fitting by a piecewise cubic polynomial.   
    Ichida, K.; Yoshimoto, F.; Kiyono, T.   
    Computing 16 (1976), no. 4, 329--338, MathSciNet.  
  46. Discrete least squares polynomial fits.    
    Shampine, L. F.    
    Comm. ACM 18 (1975), 179--180, MathSciNet.  
  47. Geometric Fit of a Monotonic Cubic (in Classroom Notes)  
    W. P. Cooke  
    American Mathematical Monthly, Vol. 80, No. 9. (Nov., 1973), pp. 1047-1051, Jstor.  
  48. Least squares piecewise cubic curve fitting.   
    Ferguson, J.; Staley, P. A.   
    Comm. ACM 16 (1973), 380--382, MathSciNet.  
  49. Parameter estimation using least-squares polynomial smoothing.    
    Budin, Michael A.    
    IEEE Trans. Systems, Man, and Cybernet. SMC-3 (1973), 371--381, MathSciNet.  
  50. A Least Squares Family of Cubic Curves with an Application to Golf Handicapping  
    Francis Scheid  
    SIAM Journal on Applied Mathematics, Vol. 22, No. 1. (Jan., 1972), pp. 77-83, Jstor.  
  51. Curve fitting with piecewise polynomials.
    Cox, M. G.
    J. Inst. Math. Appl. 8 1971 36--52, MathSciNet.  
  52. On the statistical properties of the least square interpolating polynomials.  
    Viviani, Paolo  
    Math. Biosci. 12 (1971), 81--95, MathSciNet.  
  53. Polynomial curve fitting when abscissas and ordinates are both subject to error.   
    O'Neill, M.; Sinclair, I. G.; Smith, Francis J.   
    Comput. J. 12 1969/1970 52--56, MathSciNet.  
  54. Least-Squares Fitting of a Polynomial Constrained to be Either Non-Negative Non-Decreasing or Convex  
    Derek J. Hudson  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 31, No. 1. (1969), pp. 113-118., Jstor.  
  55. On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria.  
    Powell, M. J. D.  
    Comput. J. 9 1967 404--407, MathSciNet.  
  56. Curve fitting to unequally-spaced data: Polynomial and trigonometric approximation.   
    Oliveira-Pinto, F.   
    Inst. Gulbenkian Ci. Centro Cálc. Ci. Estud. Program. Anál. Numér. No. 2 1967 47--59, MathSciNet.  
  57. The Reduction of the Variance by Least Squares Polynomial Approximations  
    H. C. Joksch  
    SIAM Review, Vol. 8, No. 2. (Apr., 1966), pp. 211-219, Jstor.  
  58. Fitting a Polynomial to Correlated Equally Spaced Observations (in Miscellanea)  
    P. Sprent  
    Biometrika, Vol. 52, No. 1/2. (Jun., 1965), pp. 275-276., Jstor.  
  59. An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation  
    Francis J. Smith  
    Mathematics of Computation, Vol. 19, No. 89. (Apr., 1965), pp. 33-36., Jstor.  
  60. Conditional Least Squares Polynomial Approximation (in Technical Notes and Short Papers)  
    R. W. Klopfenstein  
    Mathematics of Computation, Vol. 18, No. 88. (Oct., 1964), pp. 659-662, Jstor.  
  61. Least Squares Fitting of Polynomials to Irregularly Spaced Data  
    A. T. Berztiss  
    SIAM Review, Vol. 6, No. 3. (Jul., 1964), pp. 203-227, Jstor.  
  62. On a Point Arising in Polynomial Regression Fitting (in Miscellanea)  
    C. F. Crouse  
    Biometrika, Vol. 51, No. 3/4. (Dec., 1964), pp. 501-503., Jstor.  
  63. An algorithm for minimax polynomial curve-fitting of discrete data.   
    Valentine, Charles W.; Van Dine, C. Peter    
    J. Assoc. Comput. Mach. 10 1963 283--290, MathSciNet.  
  64. Note on the Curve Fitting of Discrete Data by Economization (in Technical Notes and Short Papers)  
    F. D. Burgoyne  
    Mathematics of Computation, Vol. 16, No. 80. (Oct., 1962), pp. 498-499, Jstor.  
  65. Polynomial Curve Fitting with Constraint  
    J. E. L. Peck  
    SIAM Review, Vol. 4, No. 2. (Apr., 1962), pp. 135-141, Jstor.  
  66. Precision of Least Squares Polynomial Estimates  
    Frank Proschan  
    SIAM Review, Vol. 3, No. 3. (Jul., 1961), pp. 230-236, Jstor.  
  67. Corrigenda: The Use of Orthogonal Polynomials of Positive and Negative Binomial Frequency Functions in Curve Fitting by Aitken's Method  
    H. T. Gonin  
    Biometrika, Vol. 48, No. 3/4. (Dec., 1961), p. 476, Jstor.  
  68. The Use of Orthogonal Polynomials of the Positive and Negative Binomial Frequency Functions in Curve Fitting by Aitken's Method  
    H. T. Gonin  
    Biometrika, Vol. 48, No. 1/2. (Jun., 1961), pp. 115-123., Jstor.  
  69. An Associated Polynomial for Least Squares Approximations  
    Richard Warren  
    Annals of Mathematical Statistics, Vol. 31, No. 4. (Dec., 1960), pp. 969-981, Jstor.  
  70. Curve-Fitting Matrices (in Mathematical Notes)  
    A. B. Farnell  
    American Mathematical Monthly, Vol. 66, No. 4. (Apr., 1959), pp. 297-300, Jstor.  
  71. Correction Notes: Corrections to "Approximation and Graduation According to the Principle of Least Squares by Orthogonal Polynomials"  
    Charles Jordan  
    Annals of Mathematical Statistics, Vol. 30, No. 4. (Dec., 1959), p. 1266, Jstor.  
  72. Curve-Fitting Matrices (in Mathematical Notes)  
    Herbert S. Wilf  
    American Mathematical Monthly, Vol. 65, No. 4. (Apr., 1958), pp. 272-274, Jstor.  
  73. An Application of Linear Programming to Curve Fitting  
    James E. Kelley, Jr.  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 1. (Mar., 1958), pp. 15-22., Jstor.  
  74. Computing derivatives of least square polynomials using differences.    
    Trimble, George R., Jr.    
    Tech. Note No. 898, Ballistic Research Laboratories, Aberdeen Proving Ground, Md., (1954). 7 pp, MathSciNet.  
  75. A Multiple Group Least Squares' Problem and the Significance of the Associated Orthogonal Polynomials  
    Bradford F. Kimball  
    Journal of the American Statistical Association, Vol. 48, No. 262. (Jun., 1953), pp. 320-335, Jstor.  
  76. On Least Squares Fitting by Orthonormal Polynomials Using the Choleski Method  
    S. Rushton  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 13, No. 1. (1951), pp. 92-99, Jstor.  
  77. Orthogonal Polynomial Fitting  
    John Wishart, Theocharis Metakides  
    Biometrika, Vol. 40, No. 3/4. (Dec., 1953), pp. 361-369., Jstor.  
  78. A Note on Least Squares (in Classroom Notes)  
    D. B. Houghton  
    American Mathematical Monthly, Vol. 57, No. 9. (Nov., 1950), pp. 629-631, Jstor.  
  79. Estimation of the errors of the least-squares polynomial coefficients.    
    Guest, P. G.    
    Australian J. Sci. Research. Ser. A. 3, (1950). 364--375, MathSciNet.  
  80. A Historical Note on the Method of Least Squares (in Miscellanea)  
    R. L. Plackett  
    Biometrika, Vol. 36, No. 3/4. (Dec., 1949), pp. 458-460., Jstor.  
  81. Least-squares' fitting of data by means of polynomials. Mathematical appendix by J. W. Weinberg.  
    Birge, Raymond T.  
    Rev. Modern Physics 19, (1947). 298--360, MathSciNet.  
  82. Lewis, D. C.  
    Polynomial least square approximations.  
    Amer. J. Math. 69, (1947). 273--278, MathSciNet.  
  83. Fitting Polynomial Trends to Seasonal Data by the Method of Least Squares  
    Howard L. Jones  
    Journal of the American Statistical Association, Vol. 38, No. 224. (Dec., 1943), pp. 453-465., Jstor.  
  84. The advantages in using orthogonalised terms in a polynomial for curve-fitting.   
    Satakopan, V.   
    Indian J. Phys. 17, (1943), MathSciNet.  
  85. A rapid method for calculating the least squares solution of a polynomial of degree not exceeding the fifth.  
    Kerawala, S. M.  
    Indian J. Phys. 15, (1941). 241--276, MathSciNet.  
  86. Orthogonal polynomials applied to least square fitting of weighted observations.  
    Kimball, Bradford F.  
    Ann. Math. Statistics 11, (1940). 348--352, MathSciNet.  
  87. Polynomial Approximation by the Method of Least Squares  
    H. T. Davis  
    Annals of Mathematical Statistics, Vol. 4, No. 3. (Aug., 1933), pp. 155-195., Jstor.  
  88. Approximation and Graduation According to the Principle of Least Squares by Orthogonal Polynomials  
    Charles Jordan  
    Annals of Mathematical Statistics, Vol. 3, No. 4. (Nov., 1932), pp. 257-333+335-357., Jstor.  
  89. Formulas for the Fitting of Polynomials to Data by the Method of Least Squares  
    Harold T. Davis, Voris V. Latshaw  
    The Annals of Mathematics, 2nd Ser., Vol. 31, No. 1. (Jan., 1930), pp. 52-78, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003