Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

DOI10.1007/s11075-011-9453-xzbMath1231.65082OpenAlexW1984419959MaRDI QIDQ639990

Juan-Miguel Gracia

Publication date: 11 October 2011

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10251/49340

zbMATH Keywords

algorithmsNewton's methodnonlinear equationsquasi-Newton methodspolynomial zerosinverse function of polynomialspolynomial systems zeros

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Real polynomials: location of zeros (26C10) Numerical computation of roots of polynomial equations (65H04)

Related Items (2)

An infinite family of one-step iterators for solving nonlinear equations to increase the order of convergence and a new algorithm of global convergence ⋮ A new algorithm for solving all the real roots of a nonlinear system of equations in a given feasible region

Cites Work

• Recent applications and numerical implementation of quasi-Newton methods for solving nonlinear systems of equations
• An algorithm to initialize the search of solutions of polynomial systems
• On new third-order convergent iterative formulas
• Convergence of a generalized Newton and an inexact generalized Newton algorithms for solving nonlinear equations with nondifferentiable terms
• A bibliography on roots of polynomials
• Globally convergent inexact quasi-Newton methods for solving nonlinear systems
• A classification of quasi-Newton methods
• Practical quasi-Newton methods for solving nonlinear systems
• Fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros
• Optimal and nearly optimal algorithms for approximating polynomial zeros
• Variants of Newton's method using fifth-order quadrature formulas
• Modified Newton's method for systems of nonlinear equations with singular Jacobian
• Quasi-Newton Methods, Motivation and Theory
• Solving a Polynomial Equation: Some History and Recent Progress
• A Family of Scaled Factorized Broyden-Like Methods for Nonlinear Least Squares Problems
• On Sizing and Shifting the BFGS Update within the Sized-Broyden Family of Secant Updates
• Local results for the Gauss-Newton method on constrained rank-deficient nonlinear least squares
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
• Tensor-Krylov Methods for Solving Large-Scale Systems of Nonlinear Equations

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