KELLEY
Iterative Methods for Linear and Nonlinear Equations

KELLEY is a MATLAB library which implements iterative methods for linear and nonlinear equations, by Tim Kelley.

These codes can be downloaded directly from http://www.siam.org/books/kelley/kellcode.htm

Related Data and Programs:

CSPARSE, a C library which contains iterative methods for solving linear systems.

DLAP, a FORTRAN90 library which contains iterative methods for solving linear systems.

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.

GSL, a C++ library which can perform multidimensional root-finding.

HBSMC, a dataset directory which contains files defining large sparse matrices stored in the Harwell-Boeing format.

LINPACK. a FORTRAN90 library which carries out direct methods for solving linear systems.

MGMRES, a MATLAB library which applies the restarted GMRES algorithm to solve a sparse linear system.

MM, a data directory which contains a description and examples of the Matrix Market format for storing matrices.

SPARSEKIT, a FORTRAN90 library which carries out operations on sparse matrices, including conversion between various formats.

ST, a data directory which contains a description and examples of the ST format for storing sparse matrices, which used by the C++ version of MGMRES.

SUPER_LU, a C program which applies a fast direct solution method to a sparse linear system.

TEMPLATES, a FORTRAN90 library which carries out simple versions of various iterative solvers.

TEST_MAT, a MATLAB library which defines test matrices.

TEST_NONLIN, a FORTRAN90 library which defines test cases of multidimensional nonlinear systems of 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:

For linear equations:

• gmresb.m, "brute force" GMRES method.
• gmres.m, GMRES method, requires "givapp.m" as well.
• bicgstab.m, bi-conjugate gradient stabilized method.
• tfqmr.m, TF quotient minimum residual method.
• fdkrylov.m, finite difference solver for use in Newton iterative method.
• fdgmres.m, solver called by fdkrylov.
• fdcgstab.m, solver called by fdkrylov.
• fdtfqmr.m, solver called by fdkrylov.
• pcgsol.m, preconditioned conjugate gradient method.

For nonlinear equations:

• brsol.m, locally convergent Broyden solver.
• brsola.m, Broyden-Armijo solver.
• nsol.m, basis Newton-Shamanskii solver.
• nsola.m, Newton-Krylov-Armijo solver.
• nsolgm.m, Newton-GMRES solver.

Utilities:

• diffjac.m, estimates a jacobian matrix using finite differences.
• dirder.m, computes a finite difference directional derivative.
• fish2d.m, fast Poisson solver for the unit square.
• givapp.m, applies a sequence of Givens rotations.
• isintv.m, inverse sine transform.
• parab3p.m, applies a three point parabolic model for a line search.
• sintv.m, computes sine transform
• timestamp.m, returns the YMDHMS date as a timestamp.

Examples and Tests:

• kelley_test.m, calls all the tests;
• kelley_test_output.txt, output from the tests;
• kelley_test01.m, tests GMRES on a simple -1,2,-1 matrix;
• kelley_test02.m, tests TFQMR on a simple -1,2,-1 matrix;
• kelley_test03.m, tests BICGSTAB on a simple -1,2,-1 matrix;
• kelley_test04.m, tests GMRESB on a simple -1,2,-1 matrix;
• kelley_test05.m, tests PCGSOL on a simple -1,2,-1 matrix, and uses no preconditioner;
• kelley_test06.m, tests NSOL on the Chandrasekhar function;
• atx_121.m, computes A*x, where A is the simple -1,2,-1 matrix;
• chandrasekhar.m, evaluates the Chandrasekhar function;

You can go up one level to the MATLAB source codes.