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- W4378505308 abstract "Consider the Toeplitz matrix $T_n(f)$ generated by the symbol $f(theta)=hat{f}_r e^{mathbf{i}rtheta}+hat{f}_0+hat{f}_{-s} e^{-mathbf{i}stheta}$, where $hat{f}_r, hat{f}_0, hat{f}_{-s} in mathbb{C}$ and $0<r<n,~0<s<n$. For $r=s=1$ we have the classical tridiagonal Toeplitz matrices, for which the eigenvalues and eigenvectors are known. Similarly, the eigendecompositions are known for $1<r=s$, when the generated matrices are ``symmetrically sparse tridiagonal''. In the current paper we study the eigenvalues of $T_n(f)$ for $1leq r<s$, which are ``non-symmetrically sparse tridiagonal''. We propose an algorithm which constructs one or two ad hoc matrices smaller than $T_n(f)$, whose eigenvalues are sufficient for determining the full spectrum of $T_n(f)$. The algorithm is explained through use of a conjecture for which examples and numerical experiments are reported for supporting it and for clarifying the presentation. Open problems are briefly discussed." @default.
- W4378505308 created "2023-05-27" @default.
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- W4378505308 date "2023-05-24" @default.
- W4378505308 modified "2023-09-30" @default.
- W4378505308 title "On the eigenvalues of Toeplitz matrices with two off-diagonals" @default.
- W4378505308 doi "https://doi.org/10.48550/arxiv.2305.15107" @default.
- W4378505308 hasPublicationYear "2023" @default.
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