Abstract
We are investigating spectral properties of band symmetric Toeplitz matrices (BST matrices). By giving a suitable representation of a BST matrix, we achieve separation results and multiplicity conditions for the eigenvalues of a 7°r 5-diagonal BST matrix and also structural properties of the eigenvectors. We give eigenvalue bounds for a 2 k 1-diagonal BST matrix and also necessary and sufficient conditions for positive definiteness which are easy to check. The same conditions apply in the case of block BST matrices, either with full blocks or with BST blocks. We exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a BST matrix, either for sequential or for parallel computations. Two algorithms, based on the bisection technique and Newton's method, are shown to be very fast for computing the eigenvalues of a 7− or 5-diagonal BST-matrix.
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