### A brief intro

First of all, let me introduce myself: I am Antonio Pino Robles—an Electronic Engineering student from the Basque Country—and I will be improving matrix functions in GNU Octave this summer, following Google Summer of Code program.The idea behind this is quite simple: given a square matrix $M\in \mathbb{C}^{n \times n}$ and a function $f$, GNU Octave will compute $f\left(M\right)$. You may think of them as an extension to scalar functions, i.e. starting from $f:\mathbb{C}\rightarrow \mathbb{C}$ compute $f:\mathbb{C}^{n \times n}\rightarrow \mathbb{C}^{n \times n}$. Their implementation is quite different, though. (Check Golub and van Loan's book[0] and the Short Course by Higham and Lin[1] for further info.)

Let me note that matrix functions are already part of octave: expm, logm, sqrtm in octave itself and funm, trigonometric and hyperbolic matrix functions in the Linear-Algebra Octave-Forge package. There are also GPLed toolboxes by Nicholas J. Higham, namely the mctoolbox[2] and the mftoolbox[3]; furthermore, GPLed software from the NAMF group—led by N. J. Higham at The University of Manchester—is available as well.

Hence, on a first part octave will be modified in order to run the toolboxes—as they are—smoothly , and then the existing implementations will be improved by means of updating their algorithms.

Finally, for a more detailed description of the project please refer to my octave-wiki page:

http://wiki.octave.org/User:Antonio_Pino

Agur bero bat!

[0] G.H. Golub and C.F. Van Loan. Matrix Computations, 4th Edition. The Johns Hopkins University Press, Baltimore, USA, 2013.

[1] Nicholas J. Higham and Lin Lijing, Matrix Functions: A Short Course, preprint, (2013).

[2] N. J. Higham. The Matrix Computation Toolbox. http://www.ma.man.ac.uk/~higham/mctoolbox

[3] N. J. Higham. The Matrix Function Toolbox. http://www.ma.man.ac.uk/~higham/mftoolbox

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