Evaluation of m†(h - ϵ)-1m for a large hermitian matrix h

Abstract

The matrix expression indicated in the title occurs in linear expansion methods for bound state or scattering solutions of Schrödinger's equation. A method of evaluation is described that is efficient and accurate for matrices h much larger than available random access memory in a computer. Expansion of the lower triangle of h or transposition is avoided and all matrix processing is sequential. The proposed method uses triangular decomposition of the Hermitian matrix, but avoids complex arithmetic unless the original matrix is complex. In comparison with direct use of Gaussian elimination for (h - ε{lunate})-1m the proposed method avoids an entire step of matrix processing. © 1971.