lsolve.cheby | R Documentation |
Chebyshev method - also known as Chebyshev iteration - avoids computation of inner product,
enabling distributed-memory computation to be more efficient at the cost of requiring
a priori knowledge on the range of spectrum for matrix A
.
lsolve.cheby(
A,
B,
xinit = NA,
reltol = 1e-05,
maxiter = 10000,
preconditioner = diag(ncol(A)),
adjsym = TRUE,
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 |
adjsym |
a logical; |
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.
gutknecht_chebyshev_2002Rlinsolve
## Overdetermined System
set.seed(100)
A = matrix(rnorm(10*5),nrow=10)
x = rnorm(5)
b = A%*%x
out1 = lsolve.sor(A,b,w=0.5)
out2 = lsolve.cheby(A,b)
matout = cbind(x, out1$x, out2$x);
colnames(matout) = c("original x","SOR result", "Chebyshev result")
print(matout)
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