I need to calculate the inverse of a dense matrix, with some elements taking values as high as 1e9 and some around 1e2. What would be the best method to do it?
Note:
I am more concerned about the precision of the answer rather than minimizing the computational time.
I explicitly need to find the
inverse
and not the solution of any linear systemAu=b
.
Size: The size of the matrix is below $100 \times 100$.
Formula The formula for Pade Approximation of order 3,3 can be given as:
$\left(120I_{n\times n}+60A+12A^2+A^3\right)\times\left(120I_{n\times n}-60A+12A^2-A^3\right)^{-1}$
where,
A
is the matrix whose exponential is to be found out.
This is the Pade Approximation for order 3,3. I am trying to implement a Pade approximation of order 13,13 in which the coefficient of $I_{n\times n} \text{is}$ 17643225600
Implementation: I am implementing the Pade Approximation for finding the exponential of a matrix in which I need to find the inverse of the "denominator" matrix.