Positive interpolatory quadrature rules generated by some biorthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Positive interpolatory quadrature rules generated by some biorthogonal polynomials
Interpolatory quadrature rules whose abscissas are zeros of a biorthogonal polynomial have proved to be useful, especially in numerical integration of singular integrands. However, the positivity of their weights has remained an open question, in some cases, since 1980. We present a general criterion for this positivity. As a consequence, we establish positivity of the weights in a quadrature r...
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MSC: 41A55 41A60 65B05 65B10 65B15 65D30 Keywords: Biorthogonal polynomials Numerical integration Symmetric weight functions Acceleration of convergence Levin transformation Rational approximation a b s t r a c t In this work, we derive a family of symmetric numerical quadrature formulas for finite-range integrals I[f ] = 1 −1 w(x)f (x) dx, where w(x) is a symmetric weight function. In partic...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2009
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-09-02299-6