zero_laguerre

zero_laguerre, a Fortran90 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.

Languages:

zero_laguerre is available in a Fortran90 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 (RC).

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

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

root_rc, a Fortran90 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 Fortran90 code which defines functions which can be used to test zero finders.

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_brent, a Fortran90 code which seeks a solution of a scalar nonlinear equation f(x) = 0, by Richard Brent.

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.

Reference:

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

Source Code:

Last revised on 26 March 2024.