Open AccessOrder-Independent Algorithm for the Asymptotic Stability of Complex Polynomials
Author(s) -
Ziad Zahreddine
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n5p24
Subject(s) - mathematics , polynomial , stability (learning theory) , order (exchange) , simple (philosophy) , complex quadratic polynomial , extension (predicate logic) , algebraic number , algorithm , routh–hurwitz stability criterion , mathematical analysis , computer science , philosophy , finance , epistemology , machine learning , economics , programming language
The Extended Routh Array (ERA) settles the asymptotic stability of complex polynomials. The ERA is a natural extension of the Routh Array which applies only to real polynomials. Although the ERA is a nice theoretical algorithm for stability testing, it has its limitations. Unfortunately, as the order of the polynomial increases, the size of calculations increases dramatically as will be shown below. In the current work, we offer an alternative algorithm which is basically equivalent to the ERA, but has the extra advantage of being simpler, more efficient, and easy to apply even to large order polynomials. In all the steps required in the construction of the new algorithm, only one single and simple algebraic operation is needed, which makes it a polynomial order-independent algorithm.