lsolve.bicg | R Documentation |
Biconjugate Gradient(BiCG) method is a modification of Conjugate Gradient for nonsymmetric systems using
evaluations with respect to A^T
as well as A
in matrix-vector multiplications.
For an overdetermined system where nrow(A)>ncol(A)
,
it is automatically transformed to the normal equation. Underdetermined system -
nrow(A)<ncol(A)
- is not supported. Preconditioning matrix M
, in theory, should be symmetric and positive definite
with fast computability for inverse, though it is not limited until the solver level.
lsolve.bicg(
A,
B,
xinit = NA,
reltol = 1e-05,
maxiter = 10000,
preconditioner = diag(ncol(A)),
verbose = TRUE
)
A |
an |
B |
a vector of length |
xinit |
a length- |
reltol |
tolerance level for stopping iterations. |
maxiter |
maximum number of iterations allowed. |
preconditioner |
an |
verbose |
a logical; |
a named list containing
solution; a vector of length n
or a matrix of size (n\times k)
.
the number of iterations required.
a vector of errors for stopping criterion.
watson_conjugate_1976Rlinsolve
\insertRefvoevodin_question_1983Rlinsolve
## Overdetermined System
set.seed(100)
A = matrix(rnorm(10*5),nrow=10)
x = rnorm(5)
b = A%*%x
out1 = lsolve.cg(A,b)
out2 = lsolve.bicg(A,b)
matout = cbind(matrix(x),out1$x, out2$x);
colnames(matout) = c("true x","CG result", "BiCG result")
print(matout)
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