Language Reference

EXPMATRIX Function

EXPMATRIX (matrix);

The EXPMATRIX function is part of the IMLMLIB library . Given an $n \times n$ matrix A, the EXPMATRIX function returns an $n \times n$ matrix approximating $e^ A = \sum _{k=0}^\infty \frac{A^ k}{k!}$. The function uses a Padé approximation algorithm as presented in Golub and Van Loan (1989).

Note that this module does not exponentiate each element of a matrix; for that, use the EXP function.

The following example demonstrates the EXPMATRIX function. For the matrix used in the example, $e^{tA}$ is the matrix $ \left( \begin{array}{lr} e^ t & t e^ t \\ 0 & e^ t \end{array} \right). $ You can compute the exponential matrix as follows: 

A = { 1 1, 0 1 };
t = 3;
X = ExpMatrix( t*A );
ExactAnswer = ( exp(t) || t*exp(t) ) //
( 0      ||   exp(t) );
print X, ExactAnswer;

Figure 25.126: Matrix Exponential

X
20.085537 60.256611
0 20.085537

ExactAnswer
20.085537 60.256611
0 20.085537