A computational study of the effect of matrix size and type, condition number, coefficient accuracy and computation precision on matrix-solution accuracy

Matrices occupy a central role in most physical modeling. As the size of matrices being solved increases, it is becoming more important to quantify what factors influence the accuracy of the final result. The condition number (CN) of a matrix is an important controlling factor in limiting the solution accuracy, the effect of which can be circumvented by increasing the precision of the computations. This typically involves going from single to double precision. The article reports the results from some ongoing computer experiments conducted with the goal of acquiring some insight into such questions using a compiled BASIC language (Future Basic) that permits varying the computer precision up to 240 digits (or more) through a simple configuration command. By also varying the matrix size, the accuracy to which the original matrix coefficients are computed and the matrix type and condition number, some quantitative guidelines might be developed concerning the influences of these factors on solution accuracy. The results obtained are reviewed and their implications for computational electromagnetics are discussed.