# zero_brent

zero_brent, a Fortran90 code which finds a zero of a scalar function of a scalar variable, by Richard Brent.

The method does not require the use of derivatives, and does not assume that the function is differentiable.

### Languages:

zero_brent is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version and an R version.

### Related Data and Programs:

bisection, a Fortran90 code which applies the bisection method to seek a root of f(x) over a change-of-sign interval a <= x <= b.

bisection_integer, a Fortran90 code which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].

bisection_rc, a Fortran90 code which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication.

nms, a Fortran90 code which includes versions of Brent's zero finder.

slatec, a Fortran90 code which includes the zero finder fzero().

test_zero, a Fortran90 code which defines some test functions for which zeroes can be sought.

toms419, a Fortran90 code which seeks all the roots of a polynomial with complex coefficients, commonly known as cpoly(); this is a version of ACM TOMS algorithm 419.

zero_chandrupatla, a Fortran90 code which finds a zero of a scalar function of a scalar variable, starting from a change of sign interval, using the Chandrupatla method, which can converge faster than bisection, regula falsi, or Brent's method, by Tirupathi Chandrapatla.

zero_itp, a Fortran90 code which finds a zero of a scalar function of a scalar variable, starting from a change of sign interval, using the Interpolate/Truncate/Project (ITP) method, which has faster convergence than the bisection method.

zero_muller, a Fortran90 code which seeks a root of a nonlinear equation using the Muller method, with complex arithmetic.

zero_rc, a Fortran90 code which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC).

zoomin, a Fortran90 code which includes various zero finder routines.

### Author:

Original Fortran77 version by Richard Brent; This version by John Burkardt.

### Reference:

1. Richard Brent,
Algorithms for Minimization without Derivatives,
Dover, 2002,
ISBN: 0-486-41998-3,
LC: QA402.5.B74.

### Source Code:

Last revised on 26 March 2024.