CG_RC
Conjugate Gradient Method with Reverse Communication

CG_RC is a MATLAB library which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

CG_RC is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BACKTRACK_BINARY_RC, a MATLAB library which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).

BISECTION_RC, a MATLAB library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication (RC).

CG, a MATLAB library which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric.

CG_DISTRIBUTED, a MATLAB program which implements a version of the Conjugate Gradient (CG) NAS Parallel Benchmark using distributed memory.

GAUSS_SEIDEL, a MATLAB library which implements the Gauss-Seidel iteration for linear systems.

JACOBI, a MATLAB library which implements the Jacobi iteration for solving symmetric positive definite systems of linear equations.

LOCAL_MIN_RC, a MATLAB library which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.

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

SOR, a MATLAB library which implements a simple version of the successive over-relaxation (SOR) method for the iteration solution of a linear system of equations.

ROOT_RC, a MATLAB library which seeks a solution of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.

ROOTS_RC, a MATLAB library which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (RC), by Gaston Gonnet.

SORT_RC, a MATLAB library which can sort a list of any kind of objects, using reverse communication (RC).

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

ZERO_RC, a MATLAB library which seeks a solution of a scalar nonlinear equation f(x) = 0, using reverse communication (RC), 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. Jonathan Shewchuk,
   An introduction to the conjugate gradient method without the agonizing pain, Edition 1.25, August 1994.

Source Code:

• cg_rc.m is a reverse communication conjugate gradient routine.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• timestamp.m prints the current YMDHMS date as a time stamp.
• wathen.m returns the WATHEN matrix.
• wathen_order.m returns the order of the WATHEN matrix.

Examples and Tests:

• cg_rc_test.m, a sample calling program.
• cg_rc_test01.m, uses the 1, -2, 1 matrix.
• cg_rc_test02.m, uses the Wathen matrix.
• cg_rc_test.txt, the output file.

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