Eigenvalues for tridiagonal ۳-Toeplitz matrices

In this paper, we study the eigenvalues of real tridiagonal ۳-Toeplitz matricesof different order. When the order of a tridiagonal ۳-Toeplitz matrix is n = ۳k + ۲,the eigenvalues were found explicitly. Here, we consider the distribution of eigenvaluesfor a tridiagonal ۳-Toeplitz matrix of orders n = ۳k and n = ۳k + ۱. We explain ourmethod by finding roots of a combination of Chebyshev polynomials of the secondkind. This distribution solves the eigenproblem for integer powers of such matrices.

کلیدواژه ها:

۳-Toeplitz matrix ، Chebyshev Polynomials ، Eigenvalue