An algorithm for the inversion of a discrete convolution by the partitioning method (Q1803087)

A partitioning method with partial overlapping of adjacent sections for the inversion of a long discrete conduction is proposed. Each section is processed in turn by means of cyclic convolutions. The cyclic convolutions of short sections are transformed into Toeplitz systems of equations with non-singular triangular matrices. This enables to construct fast algorithms for inversion of long convolutions without using the Fourier transformation. A detailed description of this algorithm is given. Two examples of applications of this algorithm are presented. (One misprint is noted. On p. 204 in the Russian original the matrix of the triangular system for the first section contains a wrong element.).