An Iterative-Improvement Approach to the Numerical Solution of Vector Toeplitz Systems
- 1 March 1974
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-23 (3), 320-325
- https://doi.org/10.1109/T-C.1974.223929
Abstract
This paper describes an algorithm for the approximate solution of vector Toeplitz systems via an iterative-improvement method. The algorithm exploits the special structure of Toeplitz matrices, namely, their similarity to vector circulants, and is particularly well suited for solving large systems. Sufficient convergence conditions and concrete error bounds for the iteration are presented along with an application of the routine to a problem in the design of planar digital filters for image processing.Keywords
This publication has 12 references indexed in Scilit:
- A Numerical Algorithm for Identifying Spread Functions of Shift-Invariant Imaging SystemsIEEE Transactions on Computers, 1973
- On the direct calculation of MMSE of linear realizable estimator by Toeplitz form method (Corresp.)IEEE Transactions on Information Theory, 1971
- The inversion of covariance matrices by finite Fourier transforms (Corresp.)IEEE Transactions on Information Theory, 1970
- An extension of the theorem of Kac, Murdock and Szegö to N dimensions (Corresp.)IEEE Transactions on Information Theory, 1969
- An Algorithm for the Inversion of Finite Toeplitz MatricesJournal of the Society for Industrial and Applied Mathematics, 1964
- On the Fitting of Multivariate Autoregressions, and the Approximate Canonical Factorization of a Spectral Density MatrixBiometrika, 1963
- Note on Fitting of Functions of Several Independent VariablesJournal of the Society for Industrial and Applied Mathematics, 1961
- Toeplitz Forms and Their ApplicationsPhysics Today, 1958
- COMPOSITE MATRICESThe Quarterly Journal of Mathematics, 1954
- Zur Theorie der quadratischen und bilinearen Formen von unendlichvielen VeränderlichenMathematische Annalen, 1911