Title :
Evaluating EVD and SVD errors in signal processing environments
Author :
Baker, Eugene Scott ; DeGroat, Ronald D.
Author_Institution :
Erik Jonsson Sch. of Eng. & Comput. Sci., Texas Univ., Dallas, TX, USA
Abstract :
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.
Keywords :
eigenvalues and eigenfunctions; error analysis; matrix multiplication; signal processing; singular value decomposition; stochastic processes; EVD errors; SNR; SVD errors; asymptotic upper bound; eigenvalue decomposition; error perturbations; floating point errors; matrix cross-products; noise perturbation; numerical errors; numerical precision; signal processing environments; signal to noise ratio; singular value decomposition; stochastic upper bound; Computer errors; Computer science; Design engineering; Eigenvalues and eigenfunctions; Roundoff errors; Signal processing; Signal to noise ratio; Stochastic processes; Upper bound; Working environment noise;
Conference_Titel :
Signals, Systems & Computers, 1998. Conference Record of the Thirty-Second Asilomar Conference on
Conference_Location :
Pacific Grove, CA, USA
Print_ISBN :
0-7803-5148-7
DOI :
10.1109/ACSSC.1998.751418