Recurrent calculation of convolution with given kernel and exponential approximation

Recurrent algorithms of calculation of discrete one-sided convolution of arbitrary sequence with given kernel are on the study. They are classified on the used memory involved. We are showing methods of analysis of their effectiveness. Also we are showing that calculations of linear recurrent algorithms with constant coefficients lead to method of kernel approximation by sum of exponents. We are recommending calculation method of mentioned coefficients that in real gives solution method of classical task kernel approximation determinate on equidistant grid by sum of exponents. Potentials of proposed method are demonstrated on numerical experiments also for the noisy sampled data.