Istituto di Informatica e Telematica     
Favati P. Asymptotic bit cost of quadrature formulas obtained by variable trasformation. Technical report, 1995.
In this paper the asymptotic bit operation cost of a family of quadrature formulas, very suitable for evaluation of improper integrals, is studied. More precisely we consider the family of quadrature formulas obtained by applying $k$ times the variable transformation $ x=sinh(y)$ and then the trapezoidal rule to the transformed integral. We prove that, if the integrand function is analytic in the interior part of the integration interval and approaches zero at a rate which is at least the reciprocal of a polynomial, then the bit computational cost is bounded above by a polynomial function of the number of exact digits in the result. Moreover, disregarding logarithmic terms, the double exponential transformation $(k=2)$ leads to the optimal cost among the methods of this family.
Subject G.1.4 Quadrature and Numerical Differentiation

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