The aim of long wavelength analysis is to understand the unique behaviour of terahertz (300 (iHz - 30 THz) quasi- optical s)stems, and since most THz systems have small Fresnel numbers, a modal approach to analysis is appropriate. In this paper in particular we discuss the extension of a powerful approach based on Singular Value Decomposition (SVD) [1] fir improving the efficiency of the application of Gaussian Beam Mode Analysis ((iBMA) to complex optical systems. We compare the efficiency of the SVD approach with the overlap integral approach, and also validate the technique by comparison with test cases computed using physical optics code. This work was inspired by the need for efficient numerical schemes as part of the development of a soft-ware package for quasi-optical analysis and design of terahertz systems at NUT Maynooth (MODAL).