Computing integrals with an exponential weight on the real axis in floating point arithmetic
The aim of this work is to propose a fast and reliable algorithm for computing
integrals of the type
$$\int_{-\infty}^{\infty} f(x) e^{\scriptstyle -x^2 -\frac{\scriptstyle 1}{\scriptstyle x^2}} dx,$$
where $f(x)$ is a sufficiently smooth function, in floating point arithmetic.
The algorithm is based on a product integration rule, whose rate of convergence
depends only on the regularity of $f$, since the coefficients of the rule are ``exactly'' computed by means of suitable recurrence relations here derived.
We prove stability and convergence in the space of locally continuous functions
