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Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence
Joint Authors
Saidanlu, Saeid
Aris, Nor’aini
Abd Rahman, Ali
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-03
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Saidanlu, Saeid& Aris, Nor’aini& Abd Rahman, Ali. 2012. Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-992998
Modern Language Association (MLA)
Saidanlu, Saeid…[et al.]. Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence. Journal of Applied Mathematics No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-992998
American Medical Association (AMA)
Saidanlu, Saeid& Aris, Nor’aini& Abd Rahman, Ali. Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-992998
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-992998