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.
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