Error-free solution to a Toeplitz system of equations

Author

Harms, Brian ; Keller-McNulty, Sallie

Author_Institution

Dept. of Electr. & Comput. Eng., Kansas State Univ., Manhattan, KS, USA

Volume

39

Issue

5

fYear

1991

fDate

5/1/1991 12:00:00 AM

Firstpage

1212

Lastpage

1215

Abstract

A numerical method which allows error-free computation of the solution to a Toeplitz system of equations is developed. The method requires that the system of equations have rational entries. To avoid error that is inherent in floating-point arithmetic, multiple-modulus residue arithmetic is applied to a modified version of the Levinson algorithm and to an algorithm presented by S.Y. Kung and Y.H. Hu (1983). The error-free method has a highly parallel structure and can be implemented with existing software and hardware. The exact method presented here serves as an outline for the general approach to the development of error-free solution methods

Keywords

digital arithmetic; equations; matrix algebra; numerical methods; Levinson algorithm; Toeplitz equations solution; error-free computation; error-free solution methods; exact method; multiple-modulus residue arithmetic; numerical method; signal processing; software; Digital arithmetic; Digital signal processing; Equations; Fixed-point arithmetic; Floating-point arithmetic; Hardware; Real time systems; Signal processing algorithms; Software algorithms; Statistics;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.80957

Filename

80957