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On Generating Polynomials which are Orthogonal over Several Intervals

Bernd Fischer and Gene H. Golub
Mathematics of Computation
Vol. 56, No. 194 (Apr., 1991), pp. 711-730
DOI: 10.2307/2008403
Stable URL: http://www.jstor.org/stable/2008403
Page Count: 20
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On Generating Polynomials which are Orthogonal over Several Intervals
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Abstract

We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.

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