Email RIS file
Bookmark
Report an Issue

Generalized conjugate gradient squared [electronic resource].

Published:
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 1994.
Physical Description:
pages 1, Paper 1 : digital, PDF file
Additional Creators:
National Science Foundation (U.S.) and United States. Department of Energy. Office of Scientific and Technical Information
Access Online

Availability

I Want It
I Want It

Finding items...

Restrictions on Access:
Free-to-read Unrestricted online access
Summary:
In order to solve non-symmetric linear systems of equations, the Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient method. This is what you may expect, since CGS uses the square of the BiCG polynomial. However, CGS may suffer from its erratic convergence behavior. The method may diverge or the approximate solution may be inaccurate. BiCGSTAB uses the BiCG polynomial and a product of linear factors in an attempt to smoothen the convergence. In many cases, this has proven to be very effective. Unfortunately, the convergence of BiCGSTAB may stall when a linear factor (nearly) degenerates. BiCGstab(ℓ) is designed to overcome this degeneration of linear factors. It generalizes BiCGSTAB and uses both the BiCG polynomial and a product of higher order factors. Still, CGS may converge faster than BiCGSTAB or BiCGstab(ℓ). So instead of using a product of linear or higher order factors, it may be worthwhile to look for other polynomials. Since the BiCG polynomial is based on a three term recursion, a natural choice would be a polynomial based on another three term recursion. Possibly, a suitable choice of recursion coefficients would result in method that converges faster or as fast as CGS, but less erratic. It turns out that an algorithm for such a method can easily be formulated. One particular choice for the recursion coefficients leads to CGS. Therefore one could call this algorithm generalized CGS. Another choice for the recursion coefficients leads to BiCGSTAB. It is therefore possible to mix linear factors and some polynomial based on a three term recursion. This way one may get the best of both worlds. The authors will report on their findings.
Report Numbers:
E 1.99:conf-9404305--vol.2
conf-9404305--vol.2
Subject(s):
Other Subject(s):
Note:
Published through SciTech Connect.
12/31/1994.
"conf-9404305--vol.2"
"DE96005736"
Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994.
Fokkema, D.R.; Sleijpen, G.L.G.
Front Range Scientific Computations, Inc., Boulder, CO (United States)
USDOE, Washington, DC (United States)
View MARC record | catkey: 14350423