CG
Conjugate Gradient Solver for Linear Systems


CG is a Python 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.

Licensing:

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

Languages:

CG is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

GMGSOLVE, a Python library which can apply one step of the V-cycle of the geometric multigrid method, by Mike Sussman.

SOLVE, a Python library which demonstrates how Gauss elimination can be used to solve a simple system of linear equations A*x=b.

TEST_MAT, a Python library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

WATHEN, a Python library which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Reference:

  1. Frank Beckman,
    The Solution of Linear Equations by the Conjugate Gradient Method,
    in Mathematical Methods for Digital Computers,
    edited by John Ralston, Herbert Wilf,
    Wiley, 1967,
    ISBN: 0471706892,
    LC: QA76.5.R3.
  2. Jonathan Shewchuk,
    An introduction to the conjugate gradient method without the agonizing pain, Edition 1.25, August 1994.

Source Code:

Examples and Tests:

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


Last revised on 09 July 2015.