An algorithm with guaranteed convergence for finding a zero of a function

1971/04/01 by R. P. Brent, Richard P. Brent · 12 citations
Mathematics · #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.1093/comjnl/14.4.422

Abstract

An algorithm is presented for finding a zero of a function which changes sign in a given interval. The algorithm combines linear interpolation and inverse quadratic interpolation with bisection. Convergence is usually superlinear, and is never much slower than for bisection. ALGOL 60 procedures are given.

Cited by

• End-to-End Differential Privacy in Training Deep Neural Network Classifiers
• Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
• Multi-user Pufferfish Privacy
• Hybrid Physics-ML Model for Forward Osmosis Flux with Complete Uncertainty Quantification
• Bifurcations of Highly Inclined Near Halo Orbits using Moser Regularization
• Halfpipe: a tool for analyzing metabolic labeling RNA-seq data to quantify RNA half-lives
• On the Joint Minimization of Regularization Loss Functions in Deep Variational Bayesian Methods for Attribute-Controlled Symbolic Music Generation
• Equilibrium Points and Surface Dynamics About Comet 67P/Churyumov-Gerasimenko
• Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference
• DORO: Distributional and Outlier Robust Optimization
• Maximum Likelihood Estimation of Triangular and Polygonal Distributions
• Inverse Cubic Iteration

Related

• Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
• Development of linear functional arithmetic and its application to solving problems of interval analysis
• Chebyshev Interpolation for Function in 1D
• A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration
• Zeroes and Extrema of Functions via Random Measures