solve.lu.Hermitian(a, b, tol=0, norma)
lu.Hermitian
, representing the
symmetric indefinite decomposition of a real symmetric or
complex Hermitian matrix.
b
must equal the
dimension of the matrix underlying
a
.
tol
is negative, no
condition estimation is done. Otherwise, the reciprocal one/infinity norm
condition estimate is computed and the solve or inverse computation is done
only if the condition estimate is greater than
tol
. By default,
tol = 0
.
a
,
since the default for
lu.Hermitian
is to return one/infinity norm of the
matrix as an attribute.
A
is the matrix whose symmetric-indefinite decomposition is represented
by
a
, an object of class
"Matrix"
is returned that is the solution
x
to the system of equations A %*% x = b
If
b
is not supplied, the inverse of
A
is returned.
Attributes include a copy of the call to
solve
,
and the one/infinity norm reciprocal condition estimate if
tol
is
nonnegative.
Based on the functions dsycon, dsytri, zhecon, zhetri from LAPACK (Anderson et al. 1994).
Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia.
n <- 5 a <- Matrix( rnorm(n*n), nrow = n, ncol = n) a[row(a) > col(a)] <- t(a)[row(a) > col(a)] # construct symmetric matrix class(a) <- Matrix.class(x) b <- rnorm(n) z <- lu(a) # symmetric-indefinite decomp a %*% solve(a,b) - b # residual (solve(a) %*% b) - solve(a,b)