# newton_rc

newton_rc, a MATLAB code which solves a system of nonlinear equations by Newton's method, using reverse communication (RC).

The Jacobian matrix is approximated using finite differences. A simple forward difference approximation is used here. However, this limits accuracy, and for some problems, can produce an estimate of the Jacobian that is poor, badly conditioned, or singular.

### Languages:

newton_rc is available in a FORTRAN90 version and a MATLAB version.

### Related Data and Programs:

backtrack_binary_rc, a MATLAB code which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).

bisection_rc, a MATLAB 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).

cg_rc, a MATLAB code which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).

fsolve_test, a MATLAB code which calls fsolve(), which solves systems of nonlinear equations, inspired by the fsolve() function in MATLAB, and based on the minpack() minimization package.

local_min_rc, a MATLAB code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.

root_rc, a MATLAB 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.

roots_rc, a MATLAB code which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (RC), by Gaston Gonnet.

sort_rc, a MATLAB code which can sort a list of any kind of objects, using reverse communication (RC).

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

zero_rc, a MATLAB code which seeks a solution of a scalar nonlinear equation f(x) = 0, using reverse communication (RC), by Richard Brent.

### Reference:

1. James Ortega, Werner Rheinboldt
Iterative Solution of Nonlinear Equations in Several Variables,
SIAM, 1987,
ISBN13: 978-0898714616,
LC: QA297.8.O77.
2. Werner Rheinboldt,
Methods for Solving Systems of Nonlinear Equations,
SIAM, 1998,
ISBN: 089871415X,
LC: QA214.R44.

### Source Code:

Last revised on 18 April 2021.