On quasi degree quadrature rules |
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Authors: | J. N. Lyness Luigi Gatteschi |
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Affiliation: | (1) Applied Mathematics Division, Argonne National Laboratory, 60439 Argonne, IL, USA;(2) Istituto di Calcoli Numerici, Università di Torino, Italy |
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Abstract: | Summary In this paper we examine quadrature rules for the integral which are exact for all with +d. We specify three distinct families of solutions which have properties not unlike the standard Gauss and Radau quadrature rules. For each integerd the abscissas of the quadrature rules lie within the closed integration interval and are expressed in terms of the zeros of a polynomialqd(y). These polynomialsqd(y), (d=0, 1, ...), which are not orthogonal, satisfy a three term recurrence relation of the type Qd+1(y)=(y+d+1)qd(y)–d+1yqd–1(y) and have zeros with the standard interlacing property.This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38 |
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Keywords: | AMS(MOS): 65D30 5.16 |
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