Istituto di Scienza e Tecnologie dell'Informazione     
Bini D., Capovani M. Spectral and computational properties of band symmetric Toeplitz matrices. Internal note IEI-B82-03, 1982.
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 (5)-diagonal BST-matrix and also structural properties of the eigenvectors. We give eigenvalue bounds for a 2k+1-diagonal BST-matrix and also necessary and sufficient easy to check conditions for positive definiteness. The same conditions apply in the case of block BST-matrices either with full blocks or with BST-blocks. We show 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 bisection technique and Newton' s method, are shown to be very fast for computing the eigenvalues of a 7 (5)-diagonal BST-matrix.

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