Here you may find Fortran77 subroutines for the iterative methods GMRESR and BiCGstab(ell). These are methods for the iterative solution of large and typically sparse systems of linear equations with a nonsymmetric matrix. The methods have been introduced in the following papers:

*H.A. Van der Vorst and C. Vuik*,
**GMRESR: a Family of Nested GMRES Methods**,
Numerical Linear Algebra with Applications, Vol.1(4), pp. 369-386, 1994.

*G.L.G. Sleijpen
and D.R. Fokkema*,
**BiCGstab(ell) for Linear Equations involving Unsymmetric Matrices with Complex
Spectrum**, ETNA,
1 (1993), pp. 11-32.

If you are a user of the Bi-CGSTAB iterative method, please note that BiCGstab(ell=1) will give you the Bi-CGSTAB algorithm. Moreover, this implementation is the so-called "vanilla version" of Bi-CGSTAB/BiCGstab(ell), i.e. it includes two recent important enhancements for improvement of stability and robustness:

*
G.L.G. Sleijpen and
H.A. van der Vorst*,
**Reliable updated residuals in hybrid Bi-CG methods**,
Computing 56 (1996), pp. 141-163.

*G.L.G. Sleijpen
and
H.A. van der Vorst*,
**Maintaining convergence properties of BiCGstab methods in finite precision
arithmetic**, Numerical Algorithms, 10 (1995), pp. 203-223.

**Codes:**

**GMRESR**, requires BLAS (by M. Botchev)**BiCGstab(ell)**, simple (ell<=2) version, no additional software required (by M. Botchev and D.Fokkema)**BiCGstab(ell)**, full version, requires BLAS/LAPACK (by D.Fokkema)**BiCGstab(ell)**, simple (ell<=2)**complex arithmetic**Fortran90 version, no additional software required (by M. Botchev and D. Fokkema).

Note that these Fortran codes are provided on an "as is" basis. The authors provide no warranty whatsoever, either expressed or implied, regarding the work, including warranties with respect to its merchantability or fitness for any particular purpose. Moreover, note that permission to copy all or part of this code is granted, provided that the copies are not made or distributed for resale and that proper reference to the authors is made.

Created by M. Botchev; Last modified: Mon Apr 08 15:07:22 MET 2002