C. Brezinski, A TRANSPOSE-FREE LANCZOS ORTHODIR ALGORITHM FOR LINEAR-SYSTEMS/, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(3), 1997, pp. 349-354
The method of Lanczos for solving systems of linear equations is imple
mented via recurrence relationships between formal orthogonal polynomi
als. In this Note, a new procedure for computing the coefficients of t
hese recurrence relations is proposed. In contrast with all other proc
edures, it does not make use of the transpose of the matrix of the sys
tem.