Proof of a Special Case of Shanks' Conjecture

B. D.O. Anderson; E. I. Jury

doi:10.1109/TASSP.1976.1162864

Proof of a Special Case of Shanks' Conjecture

B. D.O. Anderson, E. I. Jury

Research output: Contribution to journal › Letter › peer-review

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	574-575
Number of pages	2
Journal	IEEE Transactions on Acoustics, Speech, and Signal Processing
Volume	24
Issue number	6
DOIs	https://doi.org/10.1109/TASSP.1976.1162864
Publication status	Published - Dec 1976
Externally published	Yes

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10.1109/TASSP.1976.1162864

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AB - 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.

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ER -

Proof of a Special Case of Shanks' Conjecture

Abstract

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