## Nakamura-Tsujimoto Laboratory

Welcome to Nakamura-Tsujimoto laboratory studying *Applied Integrable Systems*.

### Research Subject: Applied Integrable Systems

Our research subjects are integrable systems and their applications to engineering science.

#### I-SVD (Integrable Singular Value Decomposition) Project

- New algorithm named the
*mdLVs*for computing matrix singular values based on discrete integrable systems

⇒ DLVS code is more accurate and faster than the today's standard codes of LAPACK. - New algorithm
*I-SVD*costing O(N^{2}) operations for computing singular value decomposition

⇒ DBDSLV code is fast and accurate in singular vectors because of the*dLV*type transformation. *Parallel dDC*is a bidiagonal SVD algorithm which has a good parallelism.

#### Integrable Systems and Orthogonal Polynomials

- Spectral transformations of orthogonal functions
- Special (hypergeometric) function solutions to discrete integrable systems
- Enumerative combinatorics: discrete integrable systems as dynamics on graphs