a string; either compute 1-norm or F-norm
approximations, or compte these exactly.
expm
logical indicating if the matrix exponential itself, which
is computed anyway, should be returned as well.
abstol, reltol
for method = "F.est", numerical >= 0,
as absolute and relative error tolerance.
give.exact
for method = "exact", specify if only the
1-norm, the Frobenius norm, or both are to be computed.
Details
method = "exact", aka Kronecker-Sylvester algorithm, computes a
Kronecker matrix of dimension n^2 x n^2 and
hence, with O(n^5) complexity, is prohibitely slow for
non-small n. It computes the exact exponential-condition
numbers for both the Frobenius and/or the 1-norm, depending on
give.exact.
The two other methods compute approximations, to these norms, i.e.,
estimate them, using algorithms from Higham, chapt.~3.4, both
with complexity O(n^3).
Value
when expm = TRUE, for method = "exact", a
list with components
expm
containing the matrix exponential, expm.Higham08(A).
expmCond(F|1)
numeric scalar, (an approximation to) the (matrix
exponential) condition number, for either the 1-norm
(expmCond1) or the Frobenius-norm (expmCondF).
When expm is false and method one of the approximations
("*.est"), the condition number is returned directly (i.e.,
numeric of length one).
Author(s)
Michael Stadelmann (final polish by Martin Maechler).