What all are the methods/algorithms to compute inverse and determinant of large matrices? Do these work for sparse matrices also?
Hello F.O. Farid,
Thank you for your valuable comment. I have some queries:
1. As you suggested to use Schur's unitary triangulation, so is it feasible to compute those unitary and complex transpose of unitary matrices ? If I even use this , with those many computations, I will only be able to get determinant, but not inverse !!!
Rather, I have used Schur's complement algorithm but it has some limitations.
2. MAPLE / MATLAB / Mathematica all packages use LU decomposition to calculate inverse of matrix, I think !!. I don't want to use in-built command.
3, 4. thank you again for providing such effective methods. I will look at those.
Dear Soni,
It is not recommended to invert a Matrix and not a good idea to do this on large matrices because inverting a matrix is a source of roudoff errors if the inverse exists. Solve the system of equations instead of inverting the matrix or use a taylor development formula for inverting a matrices expression. You can check your algorithm with the Hilbert's system of equations which becomes very ill-conditioned when the order n increases. Try to solve it and to inverse. n=7 and n=11 are the approximative limites when solving with standard algorithms and also with matlab as black boxes algorithms. Several published solving methods exist such that for sparse matrices : see on acm digital library http://dl.acm.org depending of your system (general, symmetric, ...) good luck
Hello,
Remark : the cited values are from simple to double precision.
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