This folder contains sources codes, scripts, and numerical results
related to the manuscript "Secant acceleration of sequential residual 
methods for solving large-scale nonlinear systems of equations" by 
E. G. Birgin and J. M. Mart\'{\i}nez.

The folder contains:

(a) Accelerated DF-SANE method (QR decomposition in qr.f90, the method
itself in dfsane.f90, and a main file in dfsanema.f90). File dfsane-no-diis.f90
corresponds to DF-SANE without the acceleration; while dfsane-bratu-3d.f90
is a copy of dfsane.f90 with the parameters used to solve the 3D bratu problem.
Of course, its existence is unnecessary. It is present here to simplify
running all experiments in batch in a simple way.

(b) The five problems reported in the paper are coded in problem.f90.
Files bratu-routines.f, cavity-routines.f, and pormed-routines.f contain
code taken from NITSOL distribution.

(c) A main file to solve the five problems with NITSOL (nitsolma.f90). 
Using nitsolma.f90 requires to install NITSOL. See:
 https://users.wpi.edu/~walker/NITSOL/
A local copy of the NITSOL distribution can also be found in this folder.

(d) In addition, although not being part of the paper, this folder
includes an implementation of pure Newton's method (newton.f90) and
a main file (newtonma.f90) to solve the 2D and 3D versions of the
Bratu problem considered in the paper. Using Newton requires routine
MA48 from HSL to solve nonsymmetric linear systems.

In the current folder, files

table-dfsanema.txt
table-nitsolma.txt

correspond to the results obtained with Accelerated DF-SANE and NITSOL, 
respectively.

Scripts

run-dfsanema
run-nitsolma
run-newtonma

contain instruction to compile and execute each one of the three
methods, respectively.

See the Numerical Results section of the manuscript for more details.