Precision problem with matrix inversion
07-15-2015, 06:25 AM
Post: #11
 Maro Member Posts: 67 Joined: May 2014
RE: Precision problem with matrix inversion
(07-15-2015 04:59 AM)cyrille de brébisson Wrote:  Hello,

I can only speak of the numerical mode here.
The matrix inversion and multiplication have been coded with 3 conflicting constraints:
- High precision
- 0 result elements should be 0
- n^3 (not n^4) and memory constraint

Of course, it is not possible to have all 3 at the same time.
- Calculations ARE done in 15 digit precision on a row by row, but are stored in 12 digit (for memory)
- small elements (smaller in magnitude than epsilon*min number) are transformed into 0
- n^3 algorithm

This leads to the behavior that you observed.
If you do want full precision, that is what the CAS is there for.

Cyrille

thanks Cyrille for your comment. Does that mean, that when working in Home environment (RPN):

1) Matrix on the stack: inv(1) ➝ resulting inverse matrix is OK, because inv() is actually a CAS command using full precision
2) Matrix on the stack: Shift ÷ ➝ resulting inverse matrix is NULL-matrix (not OK), because Shift ÷ is using reduced precision of numerical mode

In other words, "inv()" and "Shift ÷" are not the same in Home environment?
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