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2012 Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence
Saeid Saidanlu, Nor’aini Aris, Ali Abd Rahman
J. Appl. Math. 2012(SI11): 1-12 (2012). DOI: 10.1155/2012/167927


In all polynomial zerofinding algorithms, a good convergence requires a very good initial approximation of the exact roots. The objective of the work is to study the conditions for determining the initial approximations for an iterative matrix zerofinding method. The investigation is based on the Newbery's matrix construction which is similar to Fiedler's construction associated with a characteristic polynomial. To ensure that convergence to both the real and complex roots of polynomials can be attained, three methods are employed. It is found that the initial values for the Fiedler's companion matrix which is supplied by the Schmeisser's method give a better approximation to the solution in comparison to when working on these values using the Schmeisser's construction towards finding the solutions. In addition, empirical results suggest that a good convergence can still be attained when an initial approximation for the polynomial root is selected away from its real value while other approximations should be sufficiently close to their real values. Tables and figures on the errors that resulted from the implementation of the method are also given.


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Saeid Saidanlu. Nor’aini Aris. Ali Abd Rahman. "Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence." J. Appl. Math. 2012 (SI11) 1 - 12, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.65070
MathSciNet: MR2979468
Digital Object Identifier: 10.1155/2012/167927

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI11 • 2012
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