ROW-BY-ROW ELIMINATION METHOD FOR ALGEBRAIC LINEAR SYSTEMS OF EQUATIONS ARISING IN REACTOR MODAL APPROXIMATIONS METHODS.

A ROW-BY-ROW ELIMINATION METHOD FOR THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS ARISING FROM THE USE OF MODAL APPROXIMATION METHODS IN REACTOR PHYSICS AND SHIELDING PROBLEMS IS PROPOSED. THE SOLUTION ALGORITHM IS A MODIFICATION OF AN ESCALATOR METHOD FOR GENERAL MATRICES USED BY FILLIPOVITCH, GENERALIZING THE MORRIS ESCALATOR METHOD FOR SYMMETRIC MATRICES. THEALGORITHM IS ESPECIALLY SUITED FOR THE SOLUTION OF LINEAR SYSTEMS ARISING IN THE APPLICATION OF WEIGHTED RESIDUAL, VARIATIONAL, PROJECTIONAL AND MODAL APPROXIMATION METHODS. THE METHOD SELF-DETECTS BADLY POSED PROBLEMS BY CHECKING FOR NONSINGULARITY OF PARTITIONS OF THE MATRIX OF COEFFICIENTS.