Transpose-free Lanczos-type algorithms for nonsymmetric linear systems (Q1127055)

The Lanczos method for solving systems of linear equations is implemented by using recurrence relationships between formal orthogonal polynomials. A new procedure for computing the coefficients of the recurrence relationships is proposed which avoids the use of the transpose of the matrix of the system. The procedure is based on the recursive computation of the products of polynomials appearing in their expressions. This approach allows to implement simultaneously and at a low price a Lanczos-type product method such as CGS or the BiCGSTAB.