Spectral and computational properties of band symmetric Toeplitz matrices (Q800445)

This paper considers spectral properties of ''band symmetric Toeplitz'' (BST) matrices, i.e., of an \(n\times n\) symmetric Toeplitz matrix \((a_{ij})\) for which \(a_{ij}=0\) for \(| i-j|\geq k\), where k is the ''band width'' of the matrix, and the number of non-zero diagonals is \(2k+1\). The authors provide separation results and multiplicity conditions for the eigenvalues of BST matrices with 5 and 7 diagonals, and they provide eigenvalue bounds and positive definiteness criteria for general BST matrices. Relevant calculation methods are provided, allowing for either sequential or parallel computation.