System, method and computer program product for dense/sparse linear system solver accelerator

A linear system solving method, system, and computer program product, include calculating a matrix factorization for a matrix in a pair of matrices, in a form of a lower, a diagonal, an upper (LDU) decomposition, solving a first expression for a first value using a substitution module to create a first result, dividing the first result by values stored in the diagonal of the matrix to obtain a second result, and solving a second expression for a second value where a processing of the diagonal is skipped by using the second result.