BiCGstab(ell)

From this page you can get a FORTRAN implementation by D. Fokkema of the BiCGstab(ell) algorithm.
The BiCGstab(ell) algorithm can be used for computing  the solution x of a linear system A*x=b, where A is a square n by n matrix and b is an n-vector.The matrix can be real or complex, Hermitian or non-Hermitian, .... The algorithm is effective especially in case A is sparse and of large size.

If you are a user of the Bi-CGSTAB iterative method, please note that BiCGstab(ell=1) will give you the Bi-CGSTAB algorithm.

The BiCGstab(ell) algorithm has been introduced in

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.
The BiCGstab(ell) here uses enhancements as explained in
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.
and
G.L.G. Sleijpen and H.A. van der Vorst ,
Reliable updated residuals in hybrid Bi-CG methods,
Computing 56 (1996), pp. 141-163.



Get the BiCGstab(ell) FORTRAN code bistbl.f for real arithmetic and zbistbl for complex aritmethic (these codes by Diederik Fokkema require BLASS and LAPACK.
bcg2.f and zbcg2.f90 are version by Mike Botchev that do not need BLAS nor LAPACK. However, they both require ell to be one or two. bcg2.f uses real arithmetic and zbcg2.f90 complex. See also Botchevs page)

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.



  © Gerard L. G. Sleijpen   <G.L.G.Sleijpen@uu.nl>
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