Explicit inverse of a tridiagonal k−Toeplitz matrix
Copyright policy )Explicit inverse of a tridiagonal k−Toeplitz matrix
The paper presents explicit expressions for the entries of the inverse of a tridiagonal \(k\)-Toeplitz matrix \(A\). Conditions for the existence of \(A^{-1}\) are obtained from an explicit expression of the characteristic polynomial of \(A\). The results presented in the paper extend known results for the case when the residue \(\operatorname {mod} k\) of the order of \(A\) is equal to \(0\) or \(k-1\) [cf. \textit{L. Elsner} and \textit{R. M. Redheffer}, Numer. Math. 10, 153--161 (1967; Zbl 0166.03404)].
- University of Coimbra Portugal
- UNIVERSIDADE DE COIMBRA Portugal
inverse, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, characteristic polynomial, Toeplitz matrix, Chebyshev polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, tridiagonal matrix
inverse, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, characteristic polynomial, Toeplitz matrix, Chebyshev polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, tridiagonal matrix
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