A new class of modified line-SOR algorithms

An analytic and empirical study of a new class of efficient iterative algorithms for solving linear equation systems is performed. These algorithms, called modified SLOR algorithms (or for brevity MSLOR algorithms), are derived from the line versions of the standard SOR method by means of a preliminary elimination. Theoretical results in the form of comparison theorems are presented and the implementation of MSLOR algorithms for several difference formulas in different mesh geometries is discussed in detail. Special attention is paid to determining the “accurate” value of the optimum relaxation parameter. Numerical experiments show that these algoritms provide solutions with the rate of convergence increased in comparison with standard methods.