AN ITERATIVE FORMULA FOR SIMULTANEOUS LOCATION OF THE ZEROS OF A POLYNOMIAL
2021 ◽
Vol 5
(12)
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Keyword(s):
Needless to say that the search for efficient algorithms for determining zeros of polynomials has been continually raised in many applications. In this paper we give a cubic iteration method for determining simultaneously all the zeros of a polynomial – assumed distinct – starting with ‘reasonably close’ initial approximations – also assumed distinct. The polynomial – in question – is expressed in its Taylor series expansion in terms of the initial approximations and their correction terms. A formula with cubic rate of convergence – based on retaining terms up to 2ndorder of the expansion in the correction terms – is derived.
Keyword(s):
2011 ◽
Vol 33
(12)
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pp. 3299-3310
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Keyword(s):
2017 ◽
Vol 25
(3)
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pp. 199-214
Keyword(s):
2018 ◽
Vol 34
(4)
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pp. 561-594
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