kelley
kelley,
a MATLAB code which
implements iterative methods for linear and nonlinear equations,
by Tim Kelley.
These codes can be downloaded directly from
https://www.siam.org/books/kelley/kellcode.htm
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
kelley is available in
a MATLAB version.
Related Data and Programs:
dsp,
a data directory which
contains a description and
examples of the DSP format for storing sparse matrices,
which is used by the FORTRAN90 version of MGMRES.
hbsmc,
a dataset directory which
contains files defining large sparse matrices stored in the
HarwellBoeing format.
fsolve_test,
a MATLAB code which
calls fsolve() which
seeks the solution x of one or more nonlinear equations f(x)=0.
kelley_test
mgmres,
a MATLAB code which
applies the restarted GMRES algorithm to solve a sparse linear system.
test_mat,
a MATLAB code which
defines test matrices.
test_nonlin,
a MATLAB code which
implements test problems for the solution
of systems of nonlinear equations.
zero,
a MATLAB code which
seeks a solution of a scalar nonlinear equation f(x) = 0,
by Richard Brent.
Reference:

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.

Subramanyan Chandrasekhar,
Radiative Transfer,
Dover, 1960,
ISBN13: 9780486605906,
LC: QB461.C46.

Tim Kelley,
Iterative Methods for Linear and Nonlinear Equations,
SIAM, 2004,
ISBN: 0898713528,
LC: QA297.8.K45.

Yousef Saad,
Iterative Methods for Sparse Linear Systems,
Second Edition,
SIAM, 20003,
ISBN: 0898715342,
LC: QA188.S17.
Source Code:

arnoldi.m,
carries out the Arnoldi orthonormalization process on the
kth affine Krylov subspace.

bicgstab.m,
biconjugate gradient stabilized method for linear systems.

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

broyden_armijo.m,
BroydenArmijo solver for nonlinear systems.

cg.m,
conjugate gradient method for linear systems.

diffjac.m,
estimates a jacobian matrix using finite differences.

dirder.m,
computes a finite difference directional derivative.

fdcgstab.m,
solver called by fdkrylov.

fdgmres.m,
solver called by fdkrylov.

fdkrylov.m,
finite difference solver for use in Newton iterative method.

fdtfqmr.m,
solver called by fdkrylov.

fish2d.m,
fast Poisson solver for the unit square.

givapp.m,
applies a sequence of Givens rotations.

gmres.m,
GMRES method, requires "givapp.m" as well.

gmresa.m,
"brute force" GMRES method, classical GramSchmidt.

gmresb.m,
"brute force" GMRES method, modified GramSchmidt.

isintv.m,
inverse sine transform.

nsol.m,
basis NewtonShamanskii solver for nonlinear systems.

nsola.m,
NewtonKrylovArmijo solver for nonlinear systems.

nsolgm.m,
NewtonGMRES solver for nonlinear systems.

parab3p.m,
applies a three point parabolic model for a line search.

pcg.m,
preconditioned conjugate gradient method for linear systems.

sintv.m,
computes sine transform

tfqmr.m,
TF quotient minimum residual method for linear systems.
Last modified on 15 April 2021.