DocumentCode :
1088548
Title :
Proof of a special case of Shanks´ conjecture
Author :
Anderson, B.D.O. ; Jury, E.I.
Author_Institution :
University of Newcastle, New South Wales, Australia
Volume :
24
Issue :
6
fYear :
1976
fDate :
12/1/1976 12:00:00 AM
Firstpage :
574
Lastpage :
575
Abstract :
In 1972 Shanks conjectured that the least squares inverse of a two-dimensional polynomial is stable, and verified the conjecture numerically for certain low-degree two-dimensional polynomials. Recently the conjecture was proved false. However, in this note we prove the conjecture for all polynomials of a restricted and low degree. The key to the verification lies in utilizing the centrosymmetric properties of the Toeplitz matrix which arises in an equation yielding the coefficients of the approximate inverse.
Keywords :
Artificial intelligence; Australia; Convolution; Digital filters; Equations; Least squares approximation; Least squares methods; Linear matrix inequalities; Polynomials; Stability;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1976.1162864
Filename :
1162864
Link To Document :
بازگشت