Nonstandard Gaussian quadrature formulae based on operator values

In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorith...

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Bibliographic Details
Published in:Advances in computational mathematics 2010-05, Vol.32 (4), p.431-486
Main Authors: Milovanovic, Gradimir V, Cvetkovic, Aleksandar S
Format: Article
Language:English
Subjects:
Computation
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Gaussian
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Quadratures
Visualization
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Summary:In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear operators we obtain interesting explicit results connected with theory of orthogonal polynomials.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-009-9114-y