Conjugate Gradient Solver for Linear Systems

CG is 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.


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


CG 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:

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



  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:

Last revised on 12 December 2018.