A general iterative sparse linear solver and its parallelization for interval Newton methods (Q1904308)

A general indexed storage scheme to store sparse interval matrices is proposed. Both sequential and parallel algorithms to evaluate a general sparse Jacobian matrix are presented. An iterative interval linear solver that utilizes the proposed indexed storage scheme is presented. As the computationally most expensive procedures when using interval Newton methods to solve systems of nonlinear equations are evaluations of its Jacobian matrix and solving the corresponding interval linear systems, the algorithms proposed in this paper can be expected to improve the overall performance for interval Newton/generalized bisection methods for solving many large scale systems of nonlinear equations.