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Root distribution of complex coefficient polynomials

Published online by Cambridge University Press:  17 February 2025

T. N. Lucas
T. N. Lucas*
Affiliation:
7 Hoel Ty Nant, Llangeinor, Bridgend CF32 8HZ

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The Routh Array is known to be a very convenient way to determine the number of polynomial roots that lie in the right half of the complex plane using only the polynomial coefficients. Extensive use of this is made particularly in control system stability studies [1]. We now show that the same real-coefficient Routh algorithm can be used to obtain this information for polynomials with complex coefficients, which are prominent in areas of engineering such as electrical inductance theory [2]. The method is easy to apply and is seen to be more straightforward than existing methods for this task [e.g. 3,4]. If required, it also enables the use of appropriate root-finding methods for real-coefficient polynomials to obtain the roots of complex- coefficient polynomials.

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Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 574 , March 2025, pp. 69 - 74
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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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