The authors: Yuri Ivanovich Vinogradov (1938 year of birth), doctor of science (Physics and Mathematics) and Alexey Yurievich Vinogradov (1970 year of birth), candidate of science (Physics and Mathematics). The idea of overcoming the problems of computing by dividing an integration interval into matching sectors belongs to Y. I. Vinogradov (doctor of science /Physics and Mathematics/). His doctorate thesis was based on that material (including that idea). Proposed realization of this idea (division and matching) through matrix theory formulas i.e. by means of the matrix exponents (or by other words by means of a matrizant – the Cauchy matrix, Cauchy-Krylov functions) belongs to A. Y. Vinogradov (candidate of science /Physics and Mathematics/). AT PRESENT MOMENT THIS METHOD IS THE BEST ONE. The method was finalized in the mid October 2011 and a C++ software program (that is given in this paper as well) was finalized and checked by comparative computations on 14 November 2011.
Московский государственный технический университет имени НЭ Баумана (МГТУ им. НЭ Баумана)