Timeline for more numerically accurate inverse matrix
Current License: CC BY-SA 3.0
10 events
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| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Dec 17, 2015 at 18:29 | history | edited | Karsten7 | CC BY-SA 3.0 |
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| Dec 17, 2015 at 17:20 | comment | added | matheorem | what does maximum possible precision mean? btw, i updated my post | |
| Dec 17, 2015 at 15:04 | comment | added | Karsten7 |
@matheorem With respect to why Mma doesn't choose "CofactorExpansion", I can only cite the documentation: "For matrices with approximate real or complex numbers, the inverse is generated to the maximum possible precision given the input." "The default setting of Automatic switches among these methods depending on the matrix given." That means that the default isn't designed for your special situation, where you want to have a result with a higher precision than the input. Another reason not to use "CofactorExpansion" is that it is slower than Automatic for bigger matrices.
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| Dec 17, 2015 at 14:57 | comment | added | Karsten7 |
@matheorem With using Rationalize I didn't mean to Rationalize mat every time you use Inverse, but to Rationalize it just one. If that is possible and makes sense depends on the rest of your iteration process.
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| Dec 17, 2015 at 14:44 | history | edited | Karsten7 | CC BY-SA 3.0 |
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| Dec 17, 2015 at 12:47 | comment | added | matheorem | Oh, I just read wikiwand.com/en/Invertible_matrix#/Eigen_decomposition . It seems that cofactor expansion is the same thing as the symbolic inversion formula and should be effective only for small matrix. But numerical instability is not mentioned in wikipedia | |
| Dec 17, 2015 at 12:20 | comment | added | matheorem |
Thank you. Rationalize is not suitable for me. Because I have to repeat iteration for thousands of times and rationalize is too slow. And for Method -> "CofactorExpansion", it indeed works. But on what circumstances that we should use "CofactorExpansion"? How can we be sure that it will be suitable in later iteration process?Why mma doesn't automatically choose the right way?
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| Dec 17, 2015 at 7:59 | history | edited | Karsten7 | CC BY-SA 3.0 |
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| Dec 17, 2015 at 7:10 | history | answered | Karsten7 | CC BY-SA 3.0 |