A New Matrix Formula for the Inverse Laplace Transformation

Abstract

A new matrix formula for the inverse Laplace transformation is established. After substituting the eigenvalues and coefficients and performing some simple matrix operations, one can obtain the inverse Laplace transformation of the function in question. The regular Heaviside techniques involving partial fraction expansions, function differentiations, and so on, are avoided. Since the formula is general, it is particularly advantageous for use on high-order transfer functions; since the formula is exact, the results have no numerical errors. Hundreds of commonly used transform pairs can be replaced by this single matrix formula.