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I have a tridiagonal Toeplitz matrix whose first diagonal below main diagonal, and the first diagonal above the main diagonal have elements equal to $-1$ and the main diagonal elements are same constants except at the middle element.

Can I solve the matrix analytically using Chebyshev polynomial of the second kind?

Klangen
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Jithu Paul
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    Hy by Solve you mean what? – Toni Mhax Jul 17 '19 at 11:26
  • Sorry for the lack of clarity. The system is like, K ϕ=δ, where K is the above mentioned tridiagonal Toeplitz matrix, ϕ is the column matrix of unknowns and δ is the column matrix with first element zero and all other elements zero. So, I want to know, is it possible to solve for ϕ by using Chebyshev polynomial of the second kind. – Jithu Paul Jul 19 '19 at 14:02
  • i guess the eigenvalues of such matrices are known, $0$ is not an eigenvalue in general – Toni Mhax Jul 21 '19 at 05:30

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