cg
cg,
an Octave 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 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 MIT license
Languages:
cg is available in
a C version and
a C++ version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
cg_test
bicg,
an Octave code which
implements the biconjugate gradient method (BICG), which
estimates the solution of a large sparse nonsymmetric linear system.
cg_rc,
an Octave code which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b,
using reverse communication.
cg_squared,
an Octave code which
implements the conjugate gradient squared (CGS) method for solving
a nonsymmetric sparse linear system A*x=b.
cgne,
an Octave code which
implements the conjugate gradient method (CG) for the normal equations,
that is, a method for solving a system of linear equations of the form
A*x=b, where the matrix A is not symmetric positive definite (SPD).
In this case, it is attempted to set up and solve
the normal equations A'*A*x=A'*b.
gmres,
an Octave code which
applies the Generalized Minimum Residual (GMRES) method to
solve a nonsymmetric sparse linear system.
sor,
an Octave code which
implements a simple version of the successive overrelaxation (SOR)
method for the iteration solution of a linear system of equations.
wathen_matrix,
an Octave code 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:

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.

Jonathan Shewchuk,
An introduction to the conjugate gradient method without the
agonizing pain,
Edition 1.25, August 1994.
Source Code:

orth_random.m,
returns the ORTH_RANDOM matrix.

r8_sign.m,
returns the sign of an R8.

r83_cg.m,
uses the conjugate gradient method on an R83 system.

r83_dif2.m,
returns the DIF2 matrix in R83 format.

r83_mv.m,
multiplies an R83 matrix times an R8VEC.

r83_res.m,
computes the residual R = BA*X for R83 matrices.

r83s_cg.m,
uses the conjugate gradient method on an R83S system.

r83s_dif2.m,
returns the DIF2 matrix in R83S format.

r83s_mv.m,
multiplies an R83S matrix times an R8VEC.

r83s_res.m,
computes the residual R = BA*X for R83S matrices.

r83t_cg.m,
uses the conjugate gradient method on an R83T system.

r83t_dif2.m,
returns the DIF2 matrix in R83T format.

r83t_mv.m,
multiplies an R83T matrix times an R8VEC.

r83t_res.m,
computes the residual R = BA*X for R83T matrices.

r8ge_cg.m,
uses the conjugate gradient method on an R8GE system.

r8ge_dif2.m,
returns the DIF2 matrix in R8GE format.

r8ge_mv.m,
multiplies an R8GE matrix by an R8VEC.

r8ge_res.m,
computes the residual R = BA*X for R8GE matrices.

r8mat_house_axh.m,
computes A*H where H is a compact Householder matrix.

r8mat_print.m,
prints an R8MAT.

r8mat_print_some.m,
prints some of an R8MAT.

r8pbu_cg.m,
uses the conjugate gradient method on an R8PBU system.

r8pbu_dif2.m,
returns the DIF2 matrix in R8PBU format.

r8pbu_mv.m,
multiplies an R8PBU matrix by an R8VEC.

r8pbu_res.m,
computes the residual R = BA*X for R8PBU matrices.

r8sd_cg.m,
uses the conjugate gradient method on an R8SD linear system.

r8sd_dif2.m,
returns the DIF2 matrix in R8SD format.

r8sd_mv.m,
multiplies an R8SD matrix by an R8VEC.

r8sd_res.m,
computes the residual R = BA*X for R8SD matrices.

r8sp_cg.m,
uses the conjugate gradient method on an R8SP system.

r8sp_dif2.m,
returns the DIF2 matrix in R8SP format.

r8sp_mv.m,
multiplies an R8SP matrix by an R8VEC.

r8sp_res.m,
computes the residual R = BA*X for R8SP matrices.

r8vec_house_column.m,
defines a Householder premultiplier that "packs" a column.

r8vec_print.m,
prints an R8VEC.

spd_random.m,
returns the spd_random() matrix.
Last revised on 12 December 2018.