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

5. R. P. Brent,
An algorithm with guaranteed convergence for finding a zero of a function,
* Computer Journal* 14 (1971), 422-425.
MR 49#4234.
Abstract:
dvi (2K),
pdf (30K).

Paper:
pdf (1388K).

## 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.
## Comments

The algorithm is also described in Chapter 4 of
* Algorithms for Minimization without Derivatives*,
Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
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