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| bio | website | physics.uwa.edu.au/~styler |
|---|---|---|
| location | Melbourne, Australia | |
| age | 32 | |
| visits | member for | 2 years, 9 months |
| seen | May 14 at 12:39 | |
| stats | profile views | 96 |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica @George: Yeah, I don't think that in this case the error is anything to worry about. You can compare Eigenvalues[N[{A, B}, 50]] with N[Eigenvalues[Inverse[B].A], 50] to check. Apart from possible differences in ordering, they should be the same up to a small numerical error. |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica @J.M.: He hasn't got a good record on asking clear questions. (I probably should stop bothering trying to answer them...) |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica Or use Eigenvalues[N[{M, A}, prec]] from the very beginning - and forget about exact expressions. |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica @George: The Solve[CharacteristicPolynomial[...]] is essentially what Eigenvalues does when working with exact expressions. In general there will be no "nice" way of writing the roots of a 31st degree polynomial, so just use N[expr, prec] to get the numerical values to what ever precision you needed. |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica @George: Just use N[Root[...], prec] to get the precision (prec) that you need. In general there will be no "nice" way of writing the roots of a 31st degree polynomial. |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica I just looked at your matrices. The exact Eigenvalues[Inverse[A].M] works (took a couple of minutes on my machine) and yields Root objects of degree 31 with massive integer coefficients (~1000 digits). RootApproximant won't find these unless you use insane precision. A Root expression represents the abstract root of a polynomial. The order that they are defined in is defined in the documentation. They can be evaluated to arbitrary (within reason) precision using N[]. |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica @J.M.: {Dimensions@#, MatrixRank@#} & /@ {A, B} returns {{{33, 33}, 31}, {{33, 33}, 33}}, so B is invertible. |
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Dec 3 |
answered | How to obtain Eigenvalues with maximum precision in Mathematica |
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Dec 3 |
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How to obtain Eigenvalues with maximum precision in Mathematica You beat me to it! +1 |
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Nov 22 |
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Why Mathematica (Reduce) can't find clear solution for almost trivial inequalities? @Tamas: The $b\neq0$ assumption is not included in the $b^2>4ac$ assumption, since $c$ can be less than zero. This is (almost) clear from the image posted in my answer. PS If you're happy with the answer, press the tick button to accept it! |
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Nov 21 |
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Why Mathematica (Reduce) can't find clear solution for almost trivial inequalities? @J.M.: Sure, for one off assumptions, the explicit argument or Assumptions option or Assuming[] is best. Assuming basically just Blocks $Assumptions anyway. |
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Nov 21 |
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Why Mathematica (Reduce) can't find clear solution for almost trivial inequalities? I just noticed that this is basically what J.M. did in the comments above (although the Backsubstitution -> True was not necessary). |
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Nov 21 |
answered | Why Mathematica (Reduce) can't find clear solution for almost trivial inequalities? |
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Nov 21 |
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why have we chosen our number system to be decimal (base 10) There's a Wikipedia article on radix economy that gives the argument for base $e$ being the most efficient. |
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Nov 20 |
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Finding all vectors of $\vec{y}$ such that $\operatorname{span} \left \{ \vec{v_1}, \vec{v_2}, \vec{y} \right \} = \mathbb{R^3}$ added 101 characters in body |
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Nov 20 |
answered | Finding all vectors of $\vec{y}$ such that $\operatorname{span} \left \{ \vec{v_1}, \vec{v_2}, \vec{y} \right \} = \mathbb{R^3}$ |
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Nov 18 |
answered | Solve a function with sum in Mathematica? |
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Nov 18 |
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How to make Runge-Kutta for solving nonlinear ODE system in Mathematica @George: Finally, I keep telling you to try to reduce your problems down to the bare minimum. This is both good for you and for the forum. The act of isolating your sticking point will normally help you solve it. And if you're still stuck, you can post a nice clear question that other people can work on without having to dig through the muck for you. |
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Nov 18 |
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How to make Runge-Kutta for solving nonlinear ODE system in Mathematica @George: You really should learn how to use Mathematica for the simple examples before you try to apply it to your real work. I've been helping you since August and neither your ability to program nor your ability to ask clear questions on a forum has increased. People want to help, but are not going to do ALL of your work for you. Make your questions either interesting or short. Long, messy, stupid and frustrating questions will get downvoted or ignored. |
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Nov 17 |
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Inverse of the polylogarithm Thanks Michael, can you give some specifics? |
