Nonlinear Eigenvalue Problem via Contour Integral (Beyn's Method)¶
- Task ID:
math.beyn_contour_eigenvalue - Domain:
math - Subdomain:
numerical_linear_algebra - Status:
test - Tags:
nonlinear-eigenvalue,contour-integral,svd,beyn-method,delay-differential,transcendental
Public Summary¶
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Example B1 Prompt Excerpt¶
**Task:** Locate all eigenvalues of a nonlinear matrix function inside a specified contour.
You are given a delay-type nonlinear matrix function:
\[
T(\lambda) = T_0 + \lambda T_1 + e^{-\tau\lambda} T_2
\]
where \(T_0, T_1, T_2 \in \mathbb{C}^{m \times m}\) are provided in the `data/` folder as NumPy binary files (`T0.npy`, `T1.npy`, `T2.npy`). The matrix dimension \(m\) is between 50 and 150. The delay parameter \(\tau > 0\) is given in `contour.json`.
This is a **transcendental** eigenvalue problem (not polynomial) — the term \(e^{-\tau\lambda}\) means there are infinitely many eigenvalues in the complex plane, but only a finite number lie inside any bounded contour.
Additionally, a contour is defined in `data/contour.json`:
Notes¶
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