A parallel algorithm for solving band systems and matrix inversion

In this paper new parallel algorithms for solving a band system of linear equations with bandwidth 2m+1 and for matrix inversion of such matrix are proposed. The algorithms are based on the simultaneous computation of m band triangular systems differing from each other only at the right-hand side. Thus, a computational complexity of our algorithm for the band system is the same as of a band triangular system solver. A difference is only at the number of processors used. The application of the algorithm for solving the inversion is advantageous if this computation is a part of the solving of system and it is necessary to know only selected rows or columns of the matrix inverse.