lsolve.gmres | R Documentation |
GMRES is a generic iterative solver for a nonsymmetric system of linear equations. As its name suggests, it approximates the solution using Krylov vectors with minimal residuals.
lsolve.gmres(
A,
B,
xinit = NA,
reltol = 1e-05,
maxiter = 1000,
preconditioner = diag(ncol(A)),
restart = (ncol(A) - 1),
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 |
restart |
the number of iterations before restart. |
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.
saad_gmres:_1986Rlinsolve
## Overdetermined System
set.seed(100)
A = matrix(rnorm(10*5),nrow=10)
x = rnorm(5)
b = A%*%x
out1 = lsolve.cg(A,b)
out3_1 = lsolve.gmres(A,b,restart=2)
out3_2 = lsolve.gmres(A,b,restart=3)
out3_3 = lsolve.gmres(A,b,restart=4)
matout = cbind(matrix(x),out1$x, out3_1$x, out3_2$x, out3_3$x);
colnames(matout) = c("true x","CG", "GMRES(2)", "GMRES(3)", "GMRES(4)")
print(matout)
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