On initial conditions for the convergence of simultaneous root finding methods

DOI10.1007/BF02276878zbMath0862.65029OpenAlexW1530287661MaRDI QIDQ1924484

Miodrag S. Petković

Publication date: 25 May 1997

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02276878

zbMATH Keywords

convergencepolynomialpolynomial rootscomplex interval arithmeticcomplex rootssimultaneous rootfindingWeierstrass-Dochev methodGargantini-Henrici interval methodBörsch-Supan interval methodBörsch-Supan-Nourein methodHalley-like interval methodMaehly-Ehrlich methodsquare root interval methodsquare root methodWeierstrass interval method

Mathematics Subject Classification ID

Related Items (20)

Point estimation of simultaneous methods for solving polynomial equations: A survey. II. ⋮ On a cubically convergent derivative-free root finding method ⋮ A high order iteration formula for the simultaneous inclusion of polynomial zeros ⋮ A note on the convergence of the Weierstrass SOR method for polynomial roots ⋮ Jacobi-free and complex-free method for finding simultaneously all zeros of polynomials having only real zeros ⋮ On parallel complexity of analytic functions ⋮ Point estimation and some applications to iterative methods ⋮ A new method of increasing the order of convergence step by step ⋮ A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously ⋮ A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods ⋮ Recursive algorithm without extra function evaluations for the Jacobian matrix of Viéta's polynomial system with applications ⋮ A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey ⋮ General convergence theorems for iterative processes and applications to the Weierstrass root-finding method ⋮ On the guaranteed convergence of new two-point root-finding methods for polynomial zeros ⋮ Point estimation of a family of simultaneous zero-finding methods ⋮ On the guaranteed convergence of a cubically convergent Weierstrass-like root-finding method ⋮ On the convergence of Wang-Zheng's method ⋮ Improvement of a convergence condition for Durand-Kerner iteration ⋮ On zeros of polynomial and vector solutions of associated polynomial system from Viëta theorem

Cites Work

• On some improvements of square root iteration for polynomial complex zeros
• A note on some improvements of the simultaneous methods for determination of polynomial zeros
• On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
• On an iterative method for simultaneous inclusion of polynomial complex zeros
• On the convergence order of a modified method for simultaneous finding polynomial zeros
• An iteration formula for the simultaneous determination of the zeros of a polynomial
• Parallel Laguerre iterations: The complex case
• Weierstrass formula and zero-finding methods
• 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
• Circular arithmetic and the determination of polynomial zeros
• Zur iterativen Auflösung algebraischer Gleichungen
• On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros
• A modified Newton method for polynomials
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