THE REVERSE BORDERING METHOD

The bordering method allows recursive computation of the solution of a system of linear equations by adding one new row and one new column a t each step of the procedure. When some of the intermediate systems ar e nearly singular, it is possible, by the block bordering method, to a dd several new rows and columns simultaneously. However, in that case, the solutions of some of the intermediate systems are not computed. T he reverse bordering method allows computation of the solutions of the se systems afterwards. Such a procedure has many applications in numer ical analysis, that include orthogonal polynomials, Pade approximation , and the progressive forms of extrapolation processes.