The use of pivot ratios as a guide to stability of matrix equations arising in the method of moments

In a previous communication the authors have shown that in applying the method of moments to problems in electromagnetics the matrix condition numbers can be used to indicate regions in Which instability occurs. However, the calculation of the condition numbers requires an explicit matrix inverse which is costly. The pivot ratio, which is easily calculated from information known within the Gaussian elimination scheme, indicates instabilities as well as the condition number but without requiring an explicit inverse. A number of examples illustrating the use of the pivot ratio are presented.