kelley

kelley, an Octave code which implements iterative methods for linear and nonlinear equations, including Arnoldi iteration, Broyden's method, conjugate gradient, GMRES, Krylov iteration, Newton-Krylov nonlinear solver, line search for minimization, transpose-free quasi-minimal residual solver for sparse linear systems, 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 and an Octave version.

Related Data and Programs:

kelley_test

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 Harwell-Boeing format.

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

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

test_matrix, an Octave code which defines test matrices.

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

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

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:

• arnoldi.m, carries out the Arnoldi orthonormalization process on the k-th affine Krylov subspace.
• bicgstab.m, bi-conjugate gradient stabilized method for linear systems.
• broyden.m, locally convergent Broyden solver for nonlinear systems.
• broyden_armijo.m, Broyden-Armijo 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 Gram-Schmidt.
• gmresb.m, "brute force" GMRES method, modified Gram-Schmidt.
• isintv.m, inverse sine transform.
• nsol.m, basis Newton-Shamanskii solver for nonlinear systems.
• nsola.m, Newton-Krylov-Armijo solver for nonlinear systems.
• nsolgm.m, Newton-GMRES 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.