Evaluating EVD and SVD errors in signal processing environments

In practical signal processing environments, the error perturbations in the eigenvalue decomposition (EVD) or singular value decomposition (SVD) will be due to both noise and numerical errors. Many numerical analysts have touted the SVD as being superior to the EVD because it has less numerical error. However, these errors are often insignificant when the noise perturbation is large enough. Since the EVD is computationally cheaper to compute than the SVD, it should be used when possible. In this paper, both stochastic and asymptotic upper bound approaches are used to estimate the valid signal to noise ratio range in which an EVD should be used in place of an SVD. The results may likewise be used to calculate the required numerical precision for a given signal to noise ratio. A model for floating point errors for matrix cross-products is also developed which by itself is a useful result.