Convergence of the two-point Weierstrass root-finding method. (English) Zbl 1297.65052
Let \((\mathbb{K},|\cdot|)\) denotes an arbitrary normed field and \(\mathbb{K}[z]\) denotes the ring of polynomials (in one variable) over \(\mathbb{K}\). Let \(f \in \mathbb{K}[z]\) be a polynomial of degree \(n \geq 2\) which has \(n\) simple zeros in \(\mathbb{K}\). A new local and semilocal convergence theorems for two–point Weierstrass method for the simultaneous computation of polynomial zeros given in the article. Three numerical examples presented.
Reviewer: Michael M. Pahirya (Mukachevo)
MSC:
| 65H04 | Numerical computation of roots of polynomial equations |
| 12Y05 | Computational aspects of field theory and polynomials (MSC2010) |
| 13P05 | Polynomials, factorization in commutative rings |
| 26C10 | Real polynomials: location of zeros |
Keywords:
two–point Weierstrass method; simultaneous methods; polynomial zeros; local convergence; semilocal convergence; error estimatesReferences:
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