broyden

broyden, an Octave code which implements the Broyden iterative method for the solution of a system of nonlinear equations, assuming an initial solution estimate is fairly close, by Tim Kelley.

These codes can be downloaded directly from https://ctk.math.ncsu.edu/matlab_roots.html

Licensing:

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

Languages:

broyden is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

broyden_test

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

kelley, an Octave code which implements iterative methods for linear and nonlinear equations, by Tim Kelley;

mgmres, an Octave code which applies the restarted GMRES algorithm to solve a sparse linear system.

test_nonlin, an Octave code which implements test problems for the solution of systems of nonlinear equations.

Reference:

1. Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo, Charles Romine, Henk van der Vorst,
   Templates for the Solution of Linear Systems:
   Building Blocks for Iterative Methods,
   SIAM, 1994,
   ISBN: 0898714710,
   LC: QA297.8.T45.
2. Subramanyan Chandrasekhar,
   Radiative Transfer,
   Dover, 1960,
   ISBN13: 978-0486605906,
   LC: QB461.C46.
3. Tim Kelley,
   Iterative Methods for Linear and Nonlinear Equations,
   SIAM, 2004,
   ISBN: 0898713528,
   LC: QA297.8.K45.
4. Yousef Saad,
   Iterative Methods for Sparse Linear Systems,
   Second Edition,
   SIAM, 20003,
   ISBN: 0898715342,
   LC: QA188.S17.

Source Code:

• broyden.m, locally convergent Broyden solver for nonlinear systems.