A Block Compression Algorithm for Computing Preconditioners

To implement efficiently algorithms for the solution of large systems of linear equations in modern computer architectures, it is convenient to unravel the block structure of the coefficient matrix that is present in many applications of the physics and the engineering. This is specially important when a preconditioned iterative method is used to compute an approximate solution. Identifying such a block structure is a graph compression problem and several techniques have been studied in the literature. In this work we consider the cosine algorithm introduced by Y. Saad. This algorithm groups two rows of the matrix if the corresponding angle between them in the adjacency matrix is small enough. The modification that we propose considers also the magnitude of the nonzero entries of the rows with the aim of computing a better block partition.