Timeline for Expressing a polynomial as a sum of squares
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2022 at 2:53 | comment | added | MarcoB | Just leaving a reference to @Daniel 's new and improved code in Express polynomials as sum of squares. | |
| Jun 27, 2022 at 2:10 | comment | added | NKellira | @DanielLichtblau Yes that polynomial can be written as sum of squares, it's $(a^2+b^2+c^2)^2-3(a^3b+b^3c+c^3a)\geqslant 0.$ I posted a question here: mathematica.stackexchange.com/questions/269990/…. Thanks a lot. | |
| Jun 26, 2022 at 20:31 | comment | added | Daniel Lichtblau | @tthnew I see now that there is a problem with my code. Really more like two problems. If you pose this as a new question I'll answer with the corrected version. | |
| Jun 26, 2022 at 18:00 | comment | added | Daniel Lichtblau | @tthnew Can that polynomial be written as a sum of squares? | |
| Jun 26, 2022 at 4:54 | comment | added | NKellira | Sir, it seems not to work with for example f = a^4 - 3 a^3 b + 2 a^2 b^2 + b^4 - 3 b^3 c + 2 a^2 c^2 + 2 b^2 c^2 - 3 a c^3 + c^4 | |
| Feb 3, 2017 at 16:10 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
edited body
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| Dec 11, 2016 at 18:35 | comment | added | pizzazz | That's neat, thanks! | |
| Dec 11, 2016 at 17:06 | comment | added | J. M.'s missing motivation♦ | One could do symmetric pivoting in the semidefinite case (see e.g. Golub/van Loan) if needed, tho. Of course, that adds a bit of complication... | |
| Dec 11, 2016 at 17:02 | comment | added | Daniel Lichtblau | @J.M. There is a reason Cholesky decompositions are not used for solving the "normal equations" for a least-squares solution, in the rank-deficient case. That's exactly when the matrix in question is only psd and not pd. | |
| Dec 11, 2016 at 16:55 | comment | added | J. M.'s missing motivation♦ |
It's annoying that CholeskyDecomposition[] chokes in the positive semidefinite case; otherwise, we easily get a test for semidefiniteness for free, and is definitely cheaper than an eigendecomposition.
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| Dec 11, 2016 at 16:51 | history | edited | Daniel Lichtblau | CC BY-SA 3.0 |
added 1 character in body
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| Dec 10, 2016 at 22:38 | history | answered | Daniel Lichtblau | CC BY-SA 3.0 |