Van der Vorst's method is a development of Lanczos' iterative method for the solution of a large sparse system of linear equations. Both methods can suffer from Lanczos breakdown. The usual cure for this problem is a look-ahead method. Recently, the look-around method has been proposed, which tracks the edges of blocks in degenerate cases instead of jumping across them. Here we show how Van der Vorst's minimal residual principle can be built into the look-around method.
- C. Brezinski, M. Redivo-Zaglia and H. Sadok, New look-ahead Lanczos-type algorithms for linear systems, LMA No. 40, Lúniversit´e du Littoral, preprint (1997); Numer. Math., to appear.Google Scholar
- W. Gander, E.H. Golub and D. Gruntz, Solving linear equations by extrapolation, in: Supercomputing, Trondheim (1989), Computer Systems Science, Vol. 62 (Springer, Berlin, 1989) pp. 279–293.Google Scholar
- P.K.W. Vinsome, Orthomin, an iterative method for solving sparse sets of simultaneous linear equations, in: Proc. 4th Symp. on Reservoir Simulation (Society of Petroleum Engineers of AIME, 1976) pp. 149–159.Google Scholar