cg, a C++ code 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 symmetric positive definite (SPD) (only real, positive eigenvalues).


The computer code and data files made available on this web page are distributed under the MIT 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 C++ code which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).

SPARSE_DISPLAY, a C++ code which can read information defining a matrix of numbers and display the sparsity pattern or location of the nonzero elements using gnuplot. This operation is already available in the built-in MATLAB "spy" command.

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


  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 16 February 2020.