Loyal Durand

  1. A new numerical method for inverse Laplace transforms.

    Authors: Martin M. Block, Loyal Durand
    Subjects: Numerical Analysis
    Abstract

    In a recent Letter, we derived a very accurate and fast new algorithm for
    numerically inverting Laplace transforms, which we used in obtaining gluon
    distributions from the proton structure function $F_2^{\gamma p}(x,Q^2)$. We
    numerically inverted the function $g(s)$, $s$ being the variable in Laplace
    space, to $G(v)$, where $v$ is the variable in ordinary space. We have since
    discovered that the algorithm does not work if $g(s)\rightarrow 0$ less rapidly
    than $1/s$ as $s\rightarrow\infty$, e.g., as $1/s^\beta$ for $0<\beta<1$.

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