Eigenvalue bounds for band matrices
by
Garry J. Tee
Department of Mathematics, University of Auckland

For Hermitian band matrices with bandwidth 2u-1, eigenvalue bounds are constructed which depend upon the bandwidth but not upon the order of the matrix.

If A is positive-definite and q = maxa_ii for all i, then all eigenvalues of A are in (0, uq).

Let H be a non-zero Hermitian band matrix with all diagonal elements equal to 0. If p is a strict upper bound for the eigenvalues of H then all eigenvalues are greater than -p(u-1), and if -c is a strict lower bound for the eigenvalues of H then all eigenvalues are less than (u-1)c. If H has any eigenvalue greater than d, then it has an eigenvalue less than -d/(u-1); and if H has any eigenvalue less than -g, then it has an eigenvalue greater than g/(u-1).

Date received: September 8, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caek-12.