On the Improvement of the Solutions to a Set of Simultaneous Linear Equations using the ILLIAG

نویسنده

  • Herbert E. Salzer
چکیده

where 5 > 0, a is a constant, and F\(p) is analytic and bounded in the half plane Re(j>) > c. We assume that this condition is satisfied. Whether this condition is also sufficient for the convergence of the w-point quadrature formula to the true value of f(t) in (1), when n tends to infinity, has not been determined. The author makes use here of the fact that the convergence occurs whenever F(p) is a polynomial in 1/p without a constant term; in fact, the quadrature is exact for polynomials of degree not greater than 2n. G. Szegö [10] has shown that under quite general conditions a Gauss-Jacobi type quadrature formula which converges for polynomials also converges for a much wider class of functions. Unfortunately his theorems do not seem to apply directly to the present case because the integral (1) involves a complex valued weight function which is not of bounded variation.

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تاریخ انتشار 2010