GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.
Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave’s own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages.
GNU Octave is also freely redistributable software. You may redistribute it and/or modify it under the terms of the GNU General Public License (GPL) as published by the Free Software Foundation.
Octave was written by John W. Eaton and many others. Because Octave is free software you are encouraged to help make Octave more useful by writing and contributing additional functions for it, and by reporting any problems you may have.
All above comes from GNU Octave Website.
Install GNU Octave in Ubuntu:
GNU Octave is available in Ubuntu Software Center by default, but it’s out of date.
If you would like the latest version, download the sources from ftp://ftp.gnu.org/gnu/octave. There’s a installation guide in the archive.