Gauss-Jordan elimination method for inverse matrix

Forum|Forum|6 years ago
July 14, 2019
2 replies
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I try in Mathcad to build Gauss-Jordan method for obtaining the inverse matrix but it looks quite difficult.

It is closed to Jordan elimination method, but on the right side we consider initially (in the augmented matrix) an unit matrix. Did anyone build this method in Mathcad?

Best answer by tubar

Cool ! I see that it makes also Pivotation. The problem is solved ! I attached the file.

W

Werner_E

25-Diamond I

You may look up algorithms in "Numerical Recipes", I guess.

Writing an all purpose matrix-inverse-function and implementing it in Mathcad would require the knowledge of some "tricks" to make the algorithm as stable as possible, finding the appropriate pivot element, etc.

I am sure you can find a lot of references about this algorithm after a short internet research.

But what would be the benefit compared with Mathcads built-in algorithms, which usually are well tested, quite stable and much faster than anything implemented in Mathcads programming language?

You may be interested in this thread

https://community.ptc.com/t5/PTC-Mathcad/Gauss-Jordan-rref/td-p/273580

T

tubar

Author

1-Visitor

MAthcad fucntions are Black boxes. I want to apply just the numerical method Gauss-Jordan for the inverse of a matrix, a method that is open, transparent, and verifiable.

W

Werner_E

25-Diamond I

@tubar wrote:

MAthcad fucntions are Black boxes. I want to apply just the numerical method Gauss-Jordan for the inverse of a matrix, a method that is open, transparent, and verifiable.

So for the start you sure would need some good advice about how to implement a stable algorithm.
Many algorithm implemented natively in Mathcad were based on the ones found in the above mentioned "Numerical Recipes" -> http://www.numerical.recipes

In Prime some were exchanged for the KNITRO tool box (with no advantage as far as I can tell).

Next step would be to implement the algorithm in C or the like and turn it into a user DLL which can be used from within Mathcad.

Then you may have functions which are fully verifyable and transparent which hopefully are as fast and reliable as Mathcad's built-in at the high price of a lot of work.