Convergence of the least squares method in the uniform metric

Min'ko, A. A.; Petunin, Yu. I.

doi:10.1007/bf00970658

Sib Math J

1990

DOI: 10.1007/bf00970658

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Convergence of the least squares method in the uniform metric

A. A. Min'ko¹,

Yu. I. Petunin²

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Cited by 2 publications

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Limit relationships between Chebyshev and Hahn polynomials

Bogatskaya¹,

Min'ko²

1994

Cybern Syst Anal

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Polynomials defined on a discrete set of points or, in other words, polynomials of a discrete argument are used in many parts of mathematics, in particular in function approximation theory, and also in theoretical physics [1, 2]. One of the basic tools for the analysis of polynomials of a discrete argument is the establishment of asymptotic equality to corresponding polynomials of a continuous argument (i.e., polynomials orthogonal on a continuum of points). This approach to the study of discrete polynomials has been implemented by a number of authors. Convergence of Hahn polynomials of a discrete argument to classical Jacobi polynomials is studied in [2][3][4][5]. In this paper, we consider the convergence of Hahn polynomials with the parameters a = /3 = --1/2 and a = /3 = 1/2 to Chebyshev polynomials of the first and second kind, respectively. In distinction from [4, 5], we derive exact bounds for the difference of Chebyshev polynomials and the corresponding Hahn polynomials in various metrics and obtain recurrences for the expansion coefficients of arbitrary polynomials of a discrete argument by polynomials of a continuous argument.We start with some def'mitions.

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Limit relationships between Chebyshev and Hahn polynomials

Bogatskaya¹,

Min'ko²

1994

Cybern Syst Anal

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Least squares orthogonal polynomial regression estimation for irregular design

Popiński

2018

Communications in Statistics - Theory and Methods

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Convergence of the least squares method in the uniform metric

Cited by 2 publications

References 5 publications

Limit relationships between Chebyshev and Hahn polynomials

Limit relationships between Chebyshev and Hahn polynomials

Least squares orthogonal polynomial regression estimation for irregular design

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