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Commit 6a9cdc2c authored by Sokol Serguei's avatar Sokol Serguei
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minor doc twits

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......@@ -8,7 +8,7 @@ The goal of gmresls is to solve a least squares problem Ax\~=b for which the mat
## Installation
You can install the development version of gmresls like so:
You can install the current version of gmresls like so:
``` r
intall.package("gmres") # from CRAN
......
......@@ -21,7 +21,7 @@ gmresls(f_Ax, f_Br, b, x0 = NULL, k = 0, maxit = 0, tol = 1e-07, ...)
\item{tol}{A tolerance for solution, estimated as ||B(Ax-b)||/||Bb||, default 1.e-7}
\item{...}{Parameters passed through to f_ax and f_br}
\item{...}{Parameters passed through to f_Ax and f_Br}
}
\value{
The solution x, having the structure of Bb.
......@@ -32,11 +32,12 @@ preconditioner B: BAx=Bb (dim(B)=(n,m)).
Implemented method uses GMRES(k) with callback functions, i.e. no explicit A or B are required. GMRES can be restarted after k iterations.
}
\details{
Implemented method is equivalent to a classical GMRES(k) method with restart after constructing k basis vectors and applied to a system BAx=Bb.
Implemented method is equivalent to a classical GMRES(k) method with restart after constructing k basis vectors and applied to a square system BAx=Bb.
Dense matrices constructed and stored by this method are of size (length(x), k) and (k+1, k) where k is GMRES current basis vector number. If maxit > k, GMRES will be restarted after each k iterations
Particularity of this implementation that matrices A and B have no to be stored explicitly.
User provides just callback function mimicking their multiplication by adequate vectors.
In case of non convergence after maxit iterations, attr(x) will contain a field 'warning' with the message which will be also issued with warning()
If the operator BA is not of full rank, iterations will be stopped before reaching convergence or maxit. A warning will be emitted in this case.
}
\examples{
# prepare a 4x3 toy problem Ax=b
......
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