Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers

Yuval Bistritz

Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers

Yuval Bistritz^*

^*Corresponding author for this work

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The paper considers a Gaussian-integer preserving (GIP) form for the author's method to test whether a polynomial with complex coefficients has its zeros inside the unit-circle (is 'stable'). The GIP property describes the fact that for a polynomial with Gaussian integer (i.e. "complex integer") coefficients, the test is carried out completely over Gaussian integers. The proposed algorithm has linear growth of the size of coefficients and an implied low binary complexity. This property is advantageous for deriving simpler stability constraints on designable parameters. It can also be exploited to reduce obstruction of decision about stability that can be introduced by numerical inaccuracy when testing ill-conditioned or high degree polynomials.

Original language	English
Title of host publication	ISCAS 2006
Subtitle of host publication	2006 IEEE International Symposium on Circuits and Systems, Proceedings
Pages	4256-4260
Number of pages	5
State	Published - 2006
Event	ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems - Kos, Greece Duration: 21 May 2006 → 24 May 2006

Publication series

Name	Proceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)	0271-4310

Conference

Conference	ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems
Country/Territory	Greece
City	Kos
Period	21/05/06 → 24/05/06

Cite this

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title = "Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers",

abstract = "The paper considers a Gaussian-integer preserving (GIP) form for the author's method to test whether a polynomial with complex coefficients has its zeros inside the unit-circle (is 'stable'). The GIP property describes the fact that for a polynomial with Gaussian integer (i.e. {"}complex integer{"}) coefficients, the test is carried out completely over Gaussian integers. The proposed algorithm has linear growth of the size of coefficients and an implied low binary complexity. This property is advantageous for deriving simpler stability constraints on designable parameters. It can also be exploited to reduce obstruction of decision about stability that can be introduced by numerical inaccuracy when testing ill-conditioned or high degree polynomials.",

author = "Yuval Bistritz",

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Bistritz, Y 2006, Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers. in ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings., 1693569, Proceedings - IEEE International Symposium on Circuits and Systems, pp. 4256-4260, ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Kos, Greece, 21/05/06.

Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers. / Bistritz, Yuval.
ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings. 2006. p. 4256-4260 1693569 (Proceedings - IEEE International Symposium on Circuits and Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers

Abstract

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