a vector or a matrix whose columns give the right-hand sides for
the equations.
k
The number of columns of r and rows of x to use.
upper.tri
logical; if TRUE (default), the uppertriangular part of r is used. Otherwise, the lower
one.
...
further arguments passed to other methods
Details
The generalized Cholesky decompostion of a symmetric matrix A is
A= LD t(L) where D is diagonal, L is lower triangular,
and t(L) is the transpose of L.
These functions solve either L sqrt(D) x=b
(when upper.tri=FALSE) or sqrt(D) t(L)
x=b.
Value
The solution of the triangular system. The result will be a vector if
x is a vector and a matrix if x is a matrix.
Note that forwardsolve(L, b) is just a wrapper for
backsolve(L, b, upper.tri=FALSE).
Methods
Use showMethods(backsolve) to see all the defined methods;
the two created by the bdsmatrix library are described here:
bdsmatrix
signature=(r= "gchol") for a generalized
cholesky decomposition
bdsmatrix
signature=(r= "gchol.bdsmatrix") for the
generalize cholesky decomposition of a bdsmatrix object
Note
The bdsmatrix package promotes the base R backsolve
function to a
generic.
To see the full documentation for the default method, view backsolve
from the base package.