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flintlib / arb

Arb has been merged into FLINT -- use https://github.com/flintlib/flint/ instead
http://arblib.org/
GNU Lesser General Public License v2.1
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document Hansen/Hansen-Smith? #314

Open dimpase opened 4 years ago

dimpase commented 4 years ago

Reading Arb 2.18 manual gives an impression that none of the Hansen-Smith stuff mentioned in http://fredrikj.net/blog/2018/06/the-arb-matrix-reloaded/ is implemented in Arb. Has it never actually landed, or just the manual is outdated?

dimpase commented 4 years ago

Perhaps I can also mention that the algorithm to invert the matrix is not due to Hansen-Smith, it's in an earlier paper by Hansen alone,

E.Hansen, Interval arithmetic in matrix computations. I.
J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 308–320

As well, Hansen-Smith mostly considers exact data (the input is not interval data, that is, but exact), as Hansen mentions in 

E.Hansen. On the solution of linear algebraic equations with interval coefficients. 
Linear Algebra Appl. 2 (1969), 153–165

The latter gives an improvement to Hansen-Smith.

fredrik-johansson commented 4 years ago

The documentation for arb_mat_solve mentions the algorithm, with a citation to HS1967. What exactly is missing here?

dimpase commented 4 years ago

OK, I missed this, but arb_mat_inv does not mention anything like this, and also arb_mat_det does not. That's why I actually went to read Joris's preprint on ball arithmetic, found out about Hansen-Smith there, looked at it a bit , found other papers by Hansen, found your blog post...

dimpase commented 4 years ago

It's also not clear from the docs what you do in acb_mat_solve_precond (no references there)