This manual is the definitive guide to GNU Octave, an interactive environment for numerical computation. GNU Octave provides a convenient command-line interface for solving linear and nonlinear problems using vectors and matrices. This updated edition of the manual covers version 3 of GNU Octave, and includes documentation for new features such as sparse matrices, linear programming and computational geometry. GNU Octave is free software, distributed under the GNU General Public License (GPL). All the money raised from the sale of this book supports the development of free software. For each copy sold $1 will be donated to the GNU Octave Development Fund. About the authors: John W. Eaton is the original developer of GNU Octave.