A new computer algorithm for the reliable calculation of an ill conditioned van der Mond matrix

A new computer algorithm for the reliable calculation of an ill-conditioned van der Mond matrix (VDMM) is presented where the determinant of the VDMM is found by calculation of its minors. Two numerical examples illustrate the method's application. One, where the determinant of a third-order equation is analyzed, gives a simple illustration of the technique. The second, where the order of the equation analyzed is raised to 40, shows the advantages of the proposed method compared to the standard one.