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Artificial Fish School Algorithm for Finding the Largest Module of Roots of Polynomial

Yongquan Zhou

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Abstract

The theorem used to judge whether all roots of a polynomial are in unit circle is put forward. To transform the polynomial by the transforming parameter, and Artificial Fish School Algorithm(AFSA) for finding the minimum value of the transforming parameter which makes all the roots of the polynomial in unit circle based on the judging theorem is given. It is Artificial Fish School Algorithm for finding the largest module of roots of polynomial. Several computer simulation results show that using this algorithm to find the largest module of roots of polynomial is more efficient and feasible, and the convergent speed and the accuracy of result is higher.

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What this paper is about

The theorem used to judge whether all roots of a polynomial are in unit circle is put forward. To transform the polynomial by the transforming parameter, and Artificial Fish School Algorithm(AFSA) for finding the minimum value of the transforming parameter which makes all the roots of the polynomial in unit circle based on the judging theorem is given. It is Artificial Fish School Algorithm for finding the largest module of roots of polynomial. Several computer simulation results show that using this algorithm to find the largest module of roots of polynomial is more efficient and feasible, and the convergent speed and the accuracy of result is higher.

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Available abstract

The theorem used to judge whether all roots of a polynomial are in unit circle is put forward. To transform the polynomial by the transforming parameter, and Artificial Fish School Algorithm(AFSA) for finding the minimum value of the transforming parameter which makes all the roots of the polynomial in unit circle based on the judging theorem is given. It is Artificial Fish School Algorithm for finding the largest module of roots of polynomial. Several computer simulation results show that using this algorithm to find the largest module of roots of polynomial is more efficient and feasible, and the convergent speed and the accuracy of result is higher.

Key concepts: Unit circle, Properties of polynomial roots, Polynomial, Fish <Actinopterygii>, Computer science, Algorithm, Unit (ring theory), Wilkinson's polynomial

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