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Convergence of the least squares method in the uniform metric. (English. Russian original) Zbl 0723.65008
Sib. Math. J. 31, No. 2, 279-288 (1990); translation from Sib. Mat. Zh. 31, No. 2(180), 111-122 (1990).
See the review in Zbl 0704.65007.
MSC:
65D10 Numerical smoothing, curve fitting
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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[1] I. I. Sharapudinov, ?On the convergence of the Fourier-Chebyshev sums,? Vychisl. Mat. Mat. Fiz. Respublik. Mezhvuzov. Tematicheskii Sb.,2, pp. 275-288 (1975).
[2] I. I. Sharapudinov, ?On interpolation by the method of least squares,? in: Vychisl. Mat. Programmirovanie, MGPI, Moscow (1976), pp. 173-181.
[3] I. I. Sharapudinov, ?Some properties of polynomials orthogonal on a finite system of points,? Izv. Vuzov. Mat., No. 5, 85-88 (1983). · Zbl 0525.33008
[4] I. K. Daugavet, Introduction to the Theory of Approximation of Functions [in Russian], LGU, Leningrad (1977). · Zbl 0414.41001
[5] P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1979). · Zbl 0449.33001
[6] A. F. Nikiforov, S. K. Suslov and V. B. Uvarov, Classical Orthogonal Polynomials in a Discrete Variable [in Russian], Nauka, Moscow (1985). · Zbl 0642.33020
[7] G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Public., Providence, Rhode Island (1939); revised edition (1979).
[8] M. Abramowitz and I. A. Stegun (ed.), Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series,55, Washington, D. C. (1964). · Zbl 0171.38503
[9] Y. L. Luke, The Special Functions and their Approximations,I, II. Academic Press, New York (1969). · Zbl 0193.01701
[10] V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977). · Zbl 0481.41001
[11] E. Reingold U. Nivergelt and N. Deo, Combinatorial Algorithms. Theory and Practice, Prentice Hall, New Jersey (1977).
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