Authors: G. Mastroianni and I. Notarangelo Journal: Math. Abstract: We introduce an interpolation process based on some of the zeros of the th generalized Freud polynomial.
Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved. References [Enhancements On Off] What's this? Additional Information G. Dedicated: Dedicated to Professor J.
De BonisG. Mastroianniand M.
RussoPolynomial approximation with special doubling weightsActa Sci. Szeged 69no. MR 2. MR 3. Complexity 19no. Numerical integration and its complexity Oberwolfach, Aleksandar S. MR 5. Kasuga and R. SakaiOrthonormal polynomials with generalized Freud-type weightsJ. Theoryno. FJMS 19no. MR 8. Laurita and G. MastroianniCondition numbers in numerical methods for Fredholm integral equations of the second kindJ.
Integral Equations Appl. Levin and D. Eli Levin and Doron S. MR LubinskyA survey of weighted polynomial approximation with exponential weightsSurv. Theory 31— Lubinsky and G.Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models.
Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Skip to content. Adobe DRM. Special features of this volume: — Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations.
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Mi, Applications of compressive sensing and high-dimensional function approximation in uncertainty quantification.Approximation and Computation pp Cite as. Some quadrature rules based on the zeros of Freud polynomials are suggested to compute Cauchy principal value integrals on the real line. In this paper, the main effort is to prove the stability and the convergence of the proposed rules.
Espelid and A. Genz, eds. Davis, P. De Bonis, M. Inequalities Appl. Ditzian, Z. Springer Series in Computational Mathematics, vol. Freud, G. Gautschi, W. ACM Trans. Golub, G.
Khavin, V. Encyclopedia of Mathematical Sciences, vol. Kress, V.
Kumar, S. Levin, A. Lubinsky, D.