Author(s)

P. Favati, G. Florentino, G. Lotti & F. Romani

Abstract

This paper presents a Mathematica implementation of a recent algorithm for efficient high precision automatic quadrature. Extensive numerical testing has been performed on a comprehensive set of functions showing that our algorithm is more efficient than the built-in Mathematica Gauss-Kronrod quadrature algorithm. 1 Introduction We consider the problem of computing an approximation of a definite integral by using an automatic integration routine. In a couple of recent papers [1,2] a new algorithm was introduced (Double Adaptive Quadrature, hereafter DAQ) which is suitable for high precision adaptive automatic quadrature. The basis of DAQ, in a general adaptive scheme, is the combination of the two main strategies to improve the approximation of an integral, namely interval subdivision and application of more accurate formulas. The active subintervals are stored in a q

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