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Your search keyword '"Varying measures"' showing total 4 results
Start Over Descriptor "Varying measures" Journal constructive approximation
4 results on '"Varying measures"'

1. Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure.

Author

González Ricardo, L. G. and López Lagomasino, G.

Subjects
*ORTHOGONAL polynomials, *POLYNOMIALS
Abstract

We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on bounded nonintersecting intervals of the real line and satisfy Szegő's condition. The biorthogonal polynomials are connected with certain mixed type Hermite-Padé polynomials, which verify full orthogonality relations with respect to certain varying measures. Thus, the strong asymptotic of orthogonal polynomials with respect to varying measures plays a key role in the study. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Generalized Stieltjes Polynomials and Rational Gauss–Kronrod Quadrature.

Author

Hernández, M. Bello, de la Calle Ysern, B., and Lagomasino, G. López

Subjects
*STIELTJES integrals, *POLYNOMIALS, *GAUSSIAN quadrature formulas, *MATHEMATICAL sequences, *INTERPOLATION, *GENERALIZED integrals
Abstract

Generalized Stieltjes polynomials are introduced and their asymptotic properties outside the support of the measure are studied. As applications, we prove the convergence of sequences of interpolating rational functions, whose poles are partially fixed, to Markov functions and give an asymptotic estimate of the error of rational Gauss–Kronrod quadrature formulas when functions which are analytic on some neighborhood of the set of integration are considered. [ABSTRACT FROM AUTHOR]

Published
2004
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3. Generalized Stieltjes Polynomials and Rational Gauss?Kronrod Quadrature

Author

M. Bello Hernández, G. López Lagomasino, and B. de la Calle Ysern

Subjects
Varying measures, Matemáticas, Stieltjes polynomials, General Mathematics, Mathematical analysis, Multipoint Padé-type approximation, Gauss–Kronrod quadrature, Rational function, Tanh-sinh quadrature, Gauss–Kronrod quadrature formula, Numerical integration, Computational Mathematics, symbols.namesake, symbols, Elliptic rational functions, Gauss–Jacobi quadrature, Applied mathematics, Gaussian quadrature, Gauss-Kronrod quadrature, Analysis, Rational quadrature, Mathematics, Clenshaw–Curtis quadrature
Abstract

17 pages, no figures.-- MSC1991 codes: Primary: 42C05, 41A20, 65D32; Secondary: 30E10. MR#: MR2036643 (2004m:33021) Zbl#: Zbl 1056.42017 Generalized Stieltjes polynomials are introduced and their asymptotic properties outside the support of the measure are studied. As applications, we prove the convergence of sequences of interpolating rational functions, whose poles are partially fixed, to Markov functions and give an asymptotic estimate of the error of rational Gauss–Kronrod quadrature formulas when functions which are analytic on some neighborhood of the set of integration are considered. The work of M. Bello Hernández and B. de la Calle Ysern was partially supported by Dirección General de Enseñanza Superior (DGES) under grants BFM2000-0206-C04-03 and BFM2000-0206-C04-01, respectively. The work of G. López Lagomasino was partially supported by DGES under grant BFM2000-0206-C04-01 and by INTAS under grant 00-272. Publicado

Published
2004

4. Weak Convergence of Varying Measures and Hermite—Padé Orthogonal Polynomials

Author

G. López Lagomasino and B. de la Calle Ysern

Subjects
Varying measures, Hermite polynomials, Weak convergence, Orthogonal polynomials, Matemáticas, Mathematics::Complex Variables, General Mathematics, Mathematical analysis, Function (mathematics), Measure (mathematics), Computational Mathematics, Orthogonality, Nikishin system, Applied mathematics, Padé approximant, Borel measure, Analysis, Mathematics
Abstract

23 pages, no figures.-- MSC1991 codes: 42C05, 30E10. MR#: MR1702795 (2000j:42036) Zbl#: Zbl 1058.42503 It is known that the common denominator of the Hermite-Padé approximants of a mixed Angelesco-Nikishin system shares orthogonality relations with respect to each function in the system. It is less well known that they also satisfy full orthogonality with respect to a varying measure. This problem motivates our interest in extending the class of varying measures with respect to which weak asymptotics of orthogonal polynomials takes place. In particular, for the case of a Nikishin system, we prove weak asymptotics of the corresponding varying measures. Research by second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT. Publicado

Published
1999

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