Some simultaneous iterations for finding all zeros of a polynomial with high order convergence

DOI10.1016/S0096-3003(98)00009-5zbMath0930.65054OpenAlexW2095210218MaRDI QIDQ1294297

Shiming Zheng, Fangyu Sun

Publication date: 1 February 2000

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(98)00009-5

zbMATH Keywords

convergencenumerical exampleszeros of polynomialsLagrange interpolationsimultaneous iteration

Mathematics Subject Classification ID

Related Items (11)

On the guaranteed convergence of the fourth order simultaneous method for polynomial zeros ⋮ On a cubically convergent derivative-free root finding method ⋮ A posteriori error bound methods for the inclusion of polynomial zeros ⋮ A high order iteration formula for the simultaneous inclusion of polynomial zeros ⋮ On a modification of the Ehrlich–Aberth method for simultaneous approximation of polynomial zeros ⋮ On the guaranteed convergence of the square-root iteration method ⋮ Construction of zero-finding methods by Weierstrass functions ⋮ A new method of increasing the order of convergence step by step ⋮ A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic ⋮ On the new fourth-order methods for the simultaneous approximation of polynomial zeros ⋮ On a simultaneous method of Newton-Weierstrass' type for finding all zeros of a polynomial

Cites Work

• Unnamed Item
• An iteration formula for the simultaneous determination of the zeros of a polynomial
• On some interval methods for algebraic, exponential and trigonometric polynomials
• Iterative methods for simultaneous inclusion of polynomial zeros
• On iteration methods without derivatives for the simultaneous determination of polynomial zeros
• Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• A modified Newton method for polynomials

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