Parallel solution of block tridiagonal linear systems

The explicit structure of the inverse of a block tridiagonal matrix is presented in terms of blocks defined by linear recurrence relations. Parallel algorithms are shown which solve block second order linear recurrences without using commutativity. The parallel solution of the associated block tridiagonal linear system is then investigated. Using this theoretical background, the implementation of solving algorithms is studied both on a small number of processors and on a hypercube. The resulting complexity is given in terms of parallel steps each consisting of block operations, taking into account the cost due to interprocessor communications too.