La. Balashov et al., APPROXIMATIONS OF THE EXPONENTIAL FUNCTION AND RELATIVE CLOSENESS OF STABLE SIGNALS, Mathematics of the USSR. Sbornik, 74(2), 1993, pp. 291-307
The results presented here are based on the use of approximations of a
nalytic functions in certain questions involving numerical methods for
''physical'' equations. The concepts of relative closeness and of sta
bility of signals are introduced. A simple method is given for approxi
mate inversion of the Laplace transformation, with an estimate of the
relative error. Also, estimates are obtained for the dimensions of spa
ces in which it is possible to find approximate solutions of multidime
nsional systems of linear equations, as a function of the accuracy of
approximation and the ''size'' of the spectrum of the operator.