| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Inverse eigenvalue problems (IEPs) are problems to construct matrices with prescribed eigenvalues. Especially, it is difficult to solve IEPs for totally nonnegative (TN) matrices, where all minors are nonzero.
Nonlinear equations whose solutions are explicitly expressed are called integrable systems, and time-discretization of integrable systems are discrete integrable systems. One of typical discrete integrable systems is discrete Toda equation.
In this research, we proposed new algorithms to solve IEPs for a band TN matrix with an arbitrary bandwidth, and a TN matrix with zig-zag structure called Laurent-Jacobi matrix based on discrete two-dimensional Toda equation with a reduction condition, and discrete relativistic Toda equation, respectively.
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