Use of incomplete decomposition of the coefficient matrix in solving linear equations

Matrix incomplete decompositions are widely and successfully used in iterative methods for solving systems of linear equations. We have found that one can also solve systems of linear equations directly by using an incomplete LU decomposition of the coefficient matrix. In some special cases, the proposed method not only leads to great savings in storage space but also improves the computational efficiency; for example, when solving large systems of linear equations with banded shifted coefficient matrices. Some interesting tested subroutines are also given.