# zero_laguerre

zero_laguerre, a Python code which uses Laguerre's method to find the zero of a function. The method needs first and second derivative information. The method almost always works when the function is a polynomial.

### Licensing:

The information on this web page is distributed under the MIT license.

### Languages:

zero_laguerre is available in a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

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

bisection_rc, a Python 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 (RC).

fsolve_test, a Fortran90 code which calls fsolve(), which seeks the solution x of one or more nonlinear equations f(x)=0.

root_rc, a Python code which seeks a solution of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.

test_zero, a Python code which defines functions which can be used to test zero finders.

zero_brent, a Python code which seeks a solution of a scalar nonlinear equation f(x) = 0, by Richard Brent.

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

### Reference:

1. Joseph Traub,
Iterative Methods for the Solution of Equations,
Prentice Hall, 1964.

### Source Code:

Last revised on 26 March 2024.