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A Rapid & Precise Algorithm Finding Zeros of Polynomials
2009 Edition, September 1, 2009 - IEEE - Institute of Electrical and Electronics Engineers, Inc.
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A Neural-Network Algorithm Finding Zeros of Polynomials of High Degree
2009 Edition, November 1, 2009 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

A fast and exact neural-network algorithm is proposed to find zeros of polynomials which were not solved by the most other methods. Its convergence rule was presented and proved. The computation is carried out by simple steepest descent rule with variable...

Polynomials

A brief overview of polynomials. Polynomials are algebraic expressions that include the sum of terms containing different powers of the same variable.

Bounding Multivariate Trigonometric Polynomials
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and...

Bounding Multivariate Trigonometric Polynomials
2019 Edition, Volume 67, February 1, 2019 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and...

Properties of Chebyshev polynomials modulo pk
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Chebyshev polynomials are employed in various applications, such as cryptography and pseudorandom numbers. The sequences generated by iterating Chebyshev polynomials over finite sets should have a finite period. Therefore, determining the period is considerably important in...

Entropic Proximal Operators for Nonnegative Trigonometric Polynomials
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Signal processing applications of semidefinite optimization are often rooted in sum-of-squares representations of nonnegative trigonometric polynomials. Interior-point solvers for semidefinite optimization can handle constraints of this form with a...

High-Precision Time-of-Flight Determination Algorithm for Ultrasonic Flow Measurement
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Commercial time-of-flight (TOF) ultrasonic flowmeters (UFM) are rapidly expanding in the general industry. Among the different techniques that can be applied to determine the TOF of ultrasonic waves, the cross-correlation method presents numerous advantages, such as robustness...

Belief Propagation, Bethe Approximation and Polynomials
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief...

A Coefficient Test for Quintic Permutation Polynomials over Integer Rings
Volume PP - IEEE - Institute of Electrical and Electronics Engineers, Inc.

For selecting appropriate permutation polynomials (PPs) in practical applications, it is necessary to know the coefficients of the polynomial since a brute-force exhaustive search is impractical when the number of PPs is large. Previous results give the conditions...

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