## Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case.(English)Zbl 1398.65361

Summary: We are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters $$n$$ (i.e. the number of terms of Gaver’s formula) and $$\delta$$ (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by $$-\lceil\log_{10}(\delta)\rceil+1$$. In case of noise free data this number is arbitrarily large, as it is bounded below by $$n$$. We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach.

### MSC:

 65R32 Numerical methods for inverse problems for integral equations 44A10 Laplace transform 65Y04 Numerical algorithms for computer arithmetic, etc. 68W40 Analysis of algorithms
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### References:

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