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

1971/04/01 by R. P. Brent, Richard P. Brent · 538 citations
Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Bisection method #Combinatorics #Computer science #Convergence (economics) #Function (biology) #Geometry #Interpolation (computer graphics) #Interval (graph theory) #Inverse #Inverse function #Inverse quadratic interpolation #Iterative Methods for Nonlinear Equations #Linear interpolation #Mathematical analysis #Mathematics #Polynomial #Polynomial interpolation #Quadratic equation #Sign (mathematics) #Zero (linguistics)

paper · pdf · doi:10.1093/comjnl/14.4.422

published in The Computer Journal 14(4), 422-425 (Oxford University Press)

openalex publication_date 1971/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

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