A look-ahead algorithm for the solution of general Hankel systems (Q1326405)

The authors present a stable method for solving general nonsingular Hankel systems, using a look-ahead technique to skipover singular or ill- conditioned submatrices. The proposed approach is based on a look-ahead variant of the nonsymmetric Lanczos algorithm in terms of formally orthogonal polynomials, which then yields the look-ahead Hankel solver as a special case. Some general properties of the resulting look-ahead algorithm for formally orthogonal polynomials are proved. These results are then utilized in the implementation of the Hankel solver. Some numerical experiments for Hankel systems with ill-conditioned submatrices are reported.