scholarly journals Analysis of the Finite Precision s-Step Biconjugate Gradient Method

2014 ◽  
Author(s):  
Erin Carson ◽  
James Demmel
Keyword(s):  
Gradient Method ◽  
Finite Precision ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

The BiConjugate gradient method on GPUs

2012 ◽  
Vol 64 (1) ◽  
pp. 49-58 ◽  
Author(s):  
G. Ortega ◽  
E. M. Garzón ◽  
F. Vázquez ◽  
I. García
Keyword(s):  
Gradient Method ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1319-1324 ◽  
Author(s):  
J. Torquil Smith
Keyword(s):  
Finite Difference ◽  
Gradient Method ◽  
Preceding Paper ◽  
Finite Difference Approximation ◽  
Staggered Grid ◽  
Difference Approximation ◽  
Low Frequencies ◽  
Linear System Of Equations ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

The preceding paper derives a staggered‐grid, finite‐difference approximation applicable to electromagnetic induction in the Earth. The staggered‐grid, finite‐difference approximation results in a linear system of equations [Formula: see text]x = b, where [Formula: see text] is symmetric but not Hermitian. This is solved using the biconjugate gradient method, preconditioned with a modified, partial Cholesky decomposition of [Formula: see text]. This method takes advantage of the sparsity of [Formula: see text], and converges much more quickly than methods used previously to solve the 3-D induction problem. When simulating a conductivity model at a number of frequencies, the rate of convergence slows as frequency approaches 0. The convergence rate at low frequencies can be improved by an order of magnitude, by alternating the incomplete Cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current.

An analysis of the composite step biconjugate gradient method

1993 ◽  
Vol 66 (1) ◽  
pp. 295-319 ◽  
Author(s):  
Randolph E. Bank ◽  
Tony F. Chan
Keyword(s):  
Gradient Method ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

Variants of biconjugate gradient method for compressible Navier-Stokes solver

AIAA Journal ◽  
1995 ◽  
Vol 33 (7) ◽  
pp. 1177-1184 ◽  
Author(s):  
Herng Lin ◽  
D. Y. Yang ◽  
Ching-Chang Chieng
Keyword(s):  
Gradient Method ◽  
Navier Stokes ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

Optimal Preconditioner for the Biconjugate Gradient Method

2008 ◽  
Vol 37 (5-7) ◽  
pp. 412-436 ◽  
Author(s):  
V. P. Ginkin ◽  
S. M. Ganina ◽  
K. G. Chernov
Keyword(s):  
Gradient Method ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient
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