Open source software for numerical computation

## Scilab Toolbox Japan Contest 2011

And the winners are…

With the support of the National Institute of Informatics, the Scilab Toolbox Japan Contest is organized every year to encourage broad use of Scilab software by students in Japanese universities and colleges. 2011 edition prizewinners are now known and divided into two categories: students and general section.

## Students Section

• Grand Prize Winner: Ms. Satoko Kikkawa
MuPAT (Multiple Precision Arithmetic Toolbox)
"MuPAT" is a quadruple and octuple precision arithmetic toolbox. In MuPAT, quadruple and octuple precision arithmetic can be easily treated as well as double precision arithmetic. In addition, a high-speed implementation on Windows has been developed.
• Second Prize Winner: Mr. Yasuyuki Maeda,
Interactive estimation method of eigenvalue density
We herein consider a nonlinear eigenvalue problem. This toolbox enables to estimate the eigenvalue density interactively using stochastic method and make graph. This toolbox has GUI with Scilab 5.3.3.

## General Section

• Grand Prize Winner: Dr. Katsuhisa Ozaki
Accurate Matrix Computation Toolbox
The toolbox supports accurate functions for obtaining solutions of linear systems, eigenvalues, singular values, matrix determinant and so forth. Users can obtain the solutions by only setting a tolerance for relative error. Since all routines are developed using only Scilab built-in functions, the toolbox is independent of computational environments.
• Second Prize Winner: Dr. kinji Kimura
Accelerating Scilab function "determ"
This project aims at improving Scilab function "determ". If we get a tighter upper bound of the degree of determinants of univariate matrix polynomials, we can decrease the computing costs in "determ". We implement two upper bounds. One is computed using only degrees of polynomials in matrices, which is based on Hirota bilinear form, Hungarian algorithm (Carpaneto and Toth version), Hungarian algorithm (Munkres version) or Jonker-Volgenant algorithm. The other is computed using both degrees and coefficients of polynomials in matrices, which is based on generalized eigenvalue problem.