Hello, my name is Georgios Ouzounis and I have submitted an application on Google Summer of Code ( GSoC ) for working on GNU Octave this summer. I would like to work on the topic proposed by Pascal Dupuis : "High Precision Arithmetic Computation". After exchanging a few e-mails, he agreed on mentoring me.

Addressing the problem :

There are numerous real world examples where double precision numbers, used by Octave, are not enough. Modelling exponential behaviours as found in semiconductor materials and electrical circuits ( diodes and transistors ) or modelling weather patterns are some of these examples. All of them, end up to solving linear systems of equations where the corresponding matrices are mathematically invertible but numerically not, due to large ratio between their first and last singular values.

My proposal :

A solution of the above problem would be the creation of a new basic numerical type for Octave which will depend on GNU MPFR (

http://www.mpfr.org/ ) which is ( quoting the site ) "a C library for multiple-precision floating-point computations with correct rounding". This new numerical type will give the ability to the user to use numbers with arbitrary precision, limited of course by the machine's internal memory. This numerical type I want to implement will come with a host of algorithms upon it. Some of these algorithms will be

Singular Value Decomposition ( SVD ),

QR factorization,

Cholesky factorization ( chol ),

Inverse matrix computation,

Eigenvalues and eigenvectors calculation,

Solving linear systems,

Root of non-linear function finder ( fzero ),

Minimum value finder ( fmins ).

Benefits :

The existence of this basic numerical type can be a useful tool for GNU Octave's users and for its developers too. More users will be using Octave for their computational needs and so Octave's community will grow. The outcome of this project could be combined with packages like the Electronic Circuit Simulator and the Signal package to make them more powerful. Prompted by my experience in my university, I can say it could be also useful in robotics where high precision is needed and on weather forecasting since weather is an ill-conditioned system.

You can find more information about me at my wiki page ( wiki.octave.org/user:Gouzouni ). My nick on the IRC channel is "gouzouni" and my e-mails are ouzounis_georgios@hotmail.com ( or geo_ominous@hotmail.com, one account with 2 aliases) and geoconstructor625@gmail.com .

Comments and suggestions from other core maintainers are welcome about anticipated needs and compatibility issues of this implementation.

Thank you for your time, Regards

Ouzounis Georgios