Exact and first-order error analysis of the Schur and split Schur algorithms: Theory and practice

Glaros, Nicholas; Carayannis, George

dc.contributor.author	Glaros, Nicholas	en
dc.contributor.author	Carayannis, George	en
dc.date.accessioned	2014-03-01T01:09:52Z
dc.date.available	2014-03-01T01:09:52Z
dc.date.issued	1994	en
dc.identifier.issn	1053-587X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11224
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	Algorithms	en
dc.subject.other	Computational methods	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Correlation methods	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Mathematical models	en
dc.subject.other	Recursive functions	en
dc.subject.other	Signal filtering and prediction	en
dc.subject.other	Durbin algorithms	en
dc.subject.other	First order error analysis	en
dc.subject.other	Levinson algorithms	en
dc.subject.other	Schur algorithms	en
dc.subject.other	Split Schur algorithms	en
dc.subject.other	Toeplitz solving algorithms	en
dc.subject.other	Error analysis	en
dc.title	Exact and first-order error analysis of the Schur and split Schur algorithms: Theory and practice	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/78.301831	en
heal.identifier.secondary	http://dx.doi.org/10.1109/78.301831	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	A new analytical methodology is introduced here for fixed-point error analysis of various Toeplitz solving algorithms. The method is applied to the very useful Schur algorithm and the lately introduced split Schur algorithm. Both exact and first order error analysis are provided in this paper. The theoretical results obtained are consistent with experimentation. Besides the intrinsic symmetry of the error propagation recursive formulae, the technique presented here is capable of explaining many practical situations: For signals having a small eigenvalue spread the Schur algorithm behaves better than the split Schur in the fixed-point environment. The intermediate coefficients of the split Schur algorithm leading to the PARCOR's cannot serve as alternatives to the reflection coefficients in error sensitive applications. It is demonstrated that the error-weight vectors of the Schur propagation mechanism follow Levinson-like (second order) recursions, while the same vectors of the split Schur propagation mechanism follow split Levinson-like (third-order) recursions.	en
heal.publisher	IEEE, Piscataway, NJ, United States	en
heal.journalName	IEEE Transactions on Signal Processing	en
dc.identifier.doi	10.1109/78.301831	en
dc.identifier.isi	ISI:A1994PB60100002	en
dc.identifier.volume	42	en
dc.identifier.issue	8	en
dc.identifier.spage	1916	en
dc.identifier.epage	1938	en