Generalized conjugate gradient squared
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({ell}) 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({ell}). 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 coefficientsmore »
- Publication Date:
- OSTI Identifier:
- 219554
- Report Number(s):
- CONF-9404305--Vol.2
ON: DE96005736; TRN: 96:002321-0001
- Resource Type:
- Conference
- Resource Relation:
- Conference: Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994; Other Information: PBD: [1994]; Related Information: Is Part Of Colorado Conference on iterative methods. Volume 2; PB: 261 p.
- Research Org:
- Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; MATRICES; ITERATIVE METHODS; ASYMMETRY; CONVERGENCE; COMPUTER CALCULATIONS
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