Efficient Parallel Computations for Singular Band Matrices

. Efficient parallel algorithms are presented for singular band matrix computations over arbitrary fields --- including solving systems of linear equations, and computation of the rank and a maximal nonsingular minor of a nonsingular band matrix. The algorithms are reasonably fast: for computations of band matrices of order n and band width m they are only an O(logm log 2 log n) factor slower than the fastest known algorithms for singular (or nonsingular) band matrix computations. As well, sequential implementations of the new algorithms are asymptotically faster than previous algorithms if an asymptotically efficient matrix multiplication algorithm is used as a subroutine. 1 Introduction. Nonsingular band matrices arise in many applications involving linear systems of equations and have been well studied. Golub and van Loan [7] describe sequential algorithms for solving nonsingular banded systems of linear equations and include a bibliography of work in this area. Parallel algor..