expmmethods  R Documentation 
Compute the exponential of a matrix.
expm(x)
x 
a matrix, typically inheriting from the

The exponential of a matrix is defined as the infinite Taylor
series expm(A) = I + A + A^2/2! + A^3/3! + ...
(although this is
definitely not the way to compute it). The method for the
dgeMatrix
class uses Ward's diagonal Pade' approximation with
three step preconditioning, a recommendation from
Moler & Van Loan (1978) “Nineteen dubious ways...”.
The matrix exponential of x
.
This is a translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel A.S.Hodel@Eng.Auburn.EDU. A bug in there has been fixed by Martin Maechler.
https://en.wikipedia.org/wiki/Matrix_exponential
Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twentyfive years later. SIAM Review 45, 1, 3–49. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/S00361445024180")}
for historical reference mostly:
Moler, C. and Van Loan, C. (1978)
Nineteen dubious ways to compute the exponential of a matrix.
SIAM Review 20, 4, 801–836.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/1020098")}
Eric W. Weisstein et al. (1999) Matrix Exponential. From MathWorld, https://mathworld.wolfram.com/MatrixExponential.html
Package expm, which provides newer (in some cases
faster, more accurate) algorithms for computing the matrix
exponential via its own (nongeneric) function expm()
.
expm also implements logm()
, sqrtm()
, etc.
Generic function Schur
.
(m1 < Matrix(c(1,0,1,1), ncol = 2))
(e1 < expm(m1)) ; e < exp(1)
stopifnot(all.equal(e1@x, c(e,0,e,e), tolerance = 1e15))
(m2 < Matrix(c(49, 64, 24, 31), ncol = 2))
(e2 < expm(m2))
(m3 < Matrix(cbind(0,rbind(6*diag(3),0))))# sparse!
(e3 < expm(m3)) # upper triangular
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