Multiple Orthogonality and Applications in Numerical Integration

Gradimir V. Milovanović () and Marija P. Stanić ()
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Gradimir V. Milovanović: Mathematical Institute of the Serbian Academy of Sciences and Arts
Marija P. Stanić: University of Kragujevac

Chapter Chapter 26 in Nonlinear Analysis, 2012, pp 431-455 from Springer

Abstract: Abstract In this paper, a brief survey of multiple orthogonal polynomials defined using orthogonality conditions spread out over r different measures are given. We consider multiple orthogonal polynomials on the real line, as well as on the unit semicircle in the complex plane. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recurrence relation for ordinary orthogonal polynomials (the case r=1). A method for the numerical construction of multiple orthogonal polynomials by using the discretized Stieltjes–Gautschi procedure are presented. Also, some applications of such orthogonal systems to numerical integration are given. A numerical example is included.

Keywords: Multiple orthogonal polynomials; Recurrence relations; Numerical integration; Generalized Birkhoff–Young quadrature rules; 33D45; 42C05; 65D30 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-3498-6_26

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DOI: 10.1007/978-1-4614-3498-6_26

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