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A method of inversion of the Laplace transform. (English) Zbl 0753.65097
Let $$F$$ be the Laplace transform of $$f(t)$$ and $$F_ j=F(p_ 0+jh)$$ with $$h>0$$ and suitable large $$p_ 0$$. The author determines an approximation $$f_ k(t)=\sum^ k_{i=1}S_ ie^{-m_ it}$$ of $$f(t)$$ by means of the overdetermined system $$F_ j=\sum^ k_{i=1}S_ i/(p_ 0+jh+m_ i)$$, $$j=0,1,\dots,n$$, $$n>2k$$. The unknowns $$m_ i$$ can be determined by means of a polynomial equation of order $$k$$, so that the nonlinear system turns into a linear one for the $$S_ i$$.
Reviewer: L.Berg (Rostock)
##### MSC:
 65R10 Numerical methods for integral transforms 44A10 Laplace transform
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##### References:
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