"Estimating the Upper and Lower Bounds for the Eigenvalues of any Matrix.''

S. S. Iyengar, D. J. Kouri, G. A. Parker and D. K. Hoffman

Theor. Chem. Acc. 103, 507-517 (2000).

060 MatrixBounds.pdf

Abstract:  A method for estimating the bounds for the highest and lowest eigenvalues of a finite dimensional matrix is presented. The method is tested for the Hamiltonian matrix for several particle-in-a-box-like systems. We also provide results for the well-studied benchmark case of the ro-vibrational states of H₃,  and consider bounds obtained for a completely random non-symmetric matrix. Finally, we discuss how the error in a Chebychev expansion solution of quantum scattering depends on the error made in estimating the highest eigenvalue of the Hamiltonian matrix.

Professor Gregory A. Parker
440 West Brooks
Department of Physics and Astronomy
University of Oklahoma
Norman, OK 73019 B.S. 1973

Brigham Young University
Ph.D. 1976 Brigham Young University