lsolve.qmr | R Documentation |
Quasia-Minimal Resudial(QMR) method is another remedy of the BiCG which shows rather irregular convergence behavior. It adapts to solve the reduced tridiagonal system in a least squares sense and its convergence is known to be quite smoother than BiCG.
lsolve.qmr(
A,
B,
xinit = NA,
reltol = 1e-05,
maxiter = 1000,
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.
freund_qmr:_1991Rlinsolve
## 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)
out3 = lsolve.qmr(A,b)
matout = cbind(matrix(x),out1$x, out2$x, out3$x);
colnames(matout) = c("true x","CG result", "BiCG result", "QMR result")
print(matout)
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