Iterative solution of large linear systems with non-smooth submatrices using partial wavelet transforms and split-matrix matrix-vector multiplication

The iterative solution of large linear systems with highly irregular matrices cannot be accelerated by wavelet transformation and subsequent sparsification if the transformed matrix is still highly irregular. In this paper we show that if the irregularity of the original matrix is limited to a relatively small known set of rows or columns (as is the case in significant applications), then acceleration can be achieved by a mixed approach in which only the ‘smooth’ submatrix is transformed and iterative solution is implemented using a novel ‘split-matrix’ form of matrix–vector multiplication