A method for constructing diagonally dominant preconditioners based on Jacobi rotations

A method is presented to make a given matrix strictly diagonally dominant as much as possible based on Jacobi rotations in this paper. The strictly diagonally dominant rows are used to build a preconditioner for some iterative method. The numerical tests illustrate that the method works very well even for very ill-conditioned linear systems. y well even for very ill-conditioned linear systems.