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A systolic network for numerical integration. (English) Zbl 0881.65014

This paper presents systolic implementations of a large class of numerical integration methods having the form \[ I= c\sum^n_{k=1} w_if(x_i). \] The class \({\mathfrak M}\) of these methods includes Newton-Cotes integration (trapezoidal rule, Simpson’s rule, etc.), Gaussian integration (Gauss-Lobatto, Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite, Gauss-Chebyshew, etc.) the methods of undetermined coefficients, etc. We suppose that \(f\) is a real function given by an arithmetic expression or by tabulated data. More precisely, we present a systolic network able to compute with a constant period \[ I(k) \approx \int^{b_k}_{a_k} f_k(x)dx, \] so that \(I(k)\) is obtained by applying a prescribed rule \(r_k\in {\mathfrak M}\).

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
65Y10 Numerical algorithms for specific classes of architectures
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