Sparse multiprecision matrices, SDP and the free field

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Sparse multiprecision matrices, SDP and the free field

Konrad Schrempf
Dear Octave-Experts,

I'm mainly developing new mathematical non-commutative algebraic
theory. Right now I'm working on a complete new family of semi-
definite solvers for optimization (the preprint might be on arXiv
by the end of the year). The free field is a rather abstract ob-
ject. I do have an experimental implementation in FriCAS but con-
sider to write it in C/C++ building on GMP with an interface to
Octave (which I use for numerics).

There are two sections in http://wiki.octave.org/Projects I'm
very interested, namely »High Precision Arithmetic Computation«
and »Sparse Matrices« (mainly for semidefinite programming).
Could you please tell me briefly what the current status is and
give me some contact person for exchanging some ideas offline?

I'm very deep in programming (in ancient times I even used
assembler ;-) up to abstract mathematical modelling. But I do
not have experience with huge software projects. On the other
hand I'm very interested in bringing new mathematical theory
and algorithms to a broad audience.

I followed the discussion on matrix functions in detail and
know the difficulty because I once programmed some myself using
the book of Higham (2008). How is the status (briefly) here?
Not that I can contribute substantial development right now
due to the lack of ressources but I do have ideas for develop-
ment on a meta level, i.e. to generate high level mathematical
code ...

Thanks!


Greetings from Austria
Konrad

P.S. I would rather like to stay in the background.

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Re: Sparse multiprecision matrices, SDP and the free field

PhilipNienhuis
Konrad Schrempf wrote

> Dear Octave-Experts,
>
> I'm mainly developing new mathematical non-commutative algebraic
> theory.
> <snip>
> I followed the discussion on matrix functions in detail and
> know the difficulty because I once programmed some myself using
> the book of Higham (2008). How is the status (briefly) here?
> Not that I can contribute substantial development right now
> due to the lack of ressources but I do have ideas for develop-
> ment on a meta level, i.e. to generate high level mathematical
> code ...

AFAIK a link to the latest fum.m is in this discussion here:
http://octave.1599824.n4.nabble.com/Re-GSOC-16-Improvements-to-sqrtm-logm-and-funm-td4675180.html
and points to:
https://github.com/RickOne16/matrix

It's an .m file function but TTBOMK the intention was to rewrite it in C++.
I've seen no activity there since 2016 but note that ATM the linear-algebra
package doesn't have a dedicated maintainer so there seems to be no nudge
from that side.

The original funm.m for Octave (in the linear-algebra package) was
contributed by me back in 2000 and I maintained it for a while. I still use
it regularly (invoking modified Bessel functions) for problems where the
matrices are known to be positive (semi-)definite and have distinct
eigenvalues. I haven't tried the one on github yet as my own code Just
Works, but I intend to do that some time.

Philip




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