The Schwarzian-Newton method for solving nonlinear equations, with applications

DOI10.1090/mcom/3119zbMath1355.65068arXiv1505.01983OpenAlexW2963905881MaRDI QIDQ2953211

Javier Segura

Publication date: 4 January 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01983

zbMATH Keywords

convergenceHalley's methodnonlinear equationsgamma distributionelliptic integralsbeta distributionSchwarzian-Newton method

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical computation of solutions to single equations (65H05) Elliptic functions and integrals (33E05) Numerical approximation and evaluation of special functions (33F05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (4)

\texttt{GammaCHI}: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral) ⋮ A third-order iterative algorithm for inversion of cumulative central beta distribution ⋮ Efficient algorithms for the inversion of the cumulative central beta distribution ⋮ On the global convergence of Schröder's iterative formulae for real roots of algebraic equations

Uses Software

• DLMF
• GammaCHI

Cites Work

• \texttt{GammaCHI}: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)
• Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind
• Numerical inversion of a general incomplete elliptic integral
• New inequalities from classical Sturm theorems
• Geometric constructions of iterative functions to solve nonlinear equations
• Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method
• On Halley's Variation of Newton's Method
• Classroom Note:Geometry and Convergence of Euler's and Halley's Methods
• On the Geometry of Halley's Method
• Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios
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