ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Total Positivity

Tue 17:30–18:00, Auditorium Max Weber
Construction of totally nonnegative matrices with prescribed eigenvalues via discrete integrable systems
Kanae Akaiwa (Kyoto Sangyo University)
Joint work with Yoshimasa Nakamura (Kyoto University); Masashi Iwasaki (Kyoto Prefectural University); Hisayoshi Tsutsumi (Doshisha University); Akira Yoshida (Doshisha University); Koichi Kondo (Doshisha University)

One of important topics of inverse eigenvalue problems is to construct a matrix with prescribed eigenvalues. For example, an engineering of beam in flexural vibration actually requires construction of matrices which are members of totally nonnegative (TN) matrices whose minors are all nonnegative.

Dynamical systems are sometimes called integrable system in the case where their solutions can be explicitly expressed. A skillful discretization yields discrete integrable systems having determinant solutions. Several discrete integrable systems are shown to be useful for computing eigenvalues of matrices.

In this talk, based on discrete integrable systems, we present how to construct TN matrices with prescribed eigenvalues by finite steps.