Nonlinear matrix decompositions and an application to parallel processing

Abstract

This paper introduces several decomposition results for a class of nonlinear transforms calledlattice transforms. A lattice transform has a matrix representation in the context of minimax algebra, a matrix algebraic structure developed for operations research. A general matrix decomposition method is presented and is then extended to provide necessary and sufficient conditions for mapping a lattice transform to a limited-connection parallel architecture. An additional result, necessary and sufficient conditions for finding a decomposition of a block Toeplitz matrix with Toeplitz blocks, is also given. Prior to these results, no minimax matrix decompositions had been developed.