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Multiple Orthogonality and Applications in Numerical Integration

In: Nonlinear Analysis

Author

Listed:
  • Gradimir V. Milovanović

    (Mathematical Institute of the Serbian Academy of Sciences and Arts)

  • Marija P. Stanić

    (University of Kragujevac)

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.

Suggested Citation

  • Gradimir V. Milovanović & Marija P. Stanić, 2012. "Multiple Orthogonality and Applications in Numerical Integration," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 431-455, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_26
    DOI: 10.1007/978-1-4614-3498-6_26
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