# cg_rc

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

### 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 python code which carries out a backtrack search for a set of binary decisions, using reverse communication (rc).

bisection_rc, a python code 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 python 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.

jacobi, a python code which implements the jacobi iteration for solving symmetric positive definite (spd) systems of linear equations.

local_min_rc, a python code 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.

root_rc, a python code 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 python code which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (rc), by gaston gonnet.

sort_rc, a python code which can sort a list of any kind of objects, using reverse communication (rc).

zero_rc, a python code 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:

Last revised on 20 January 2020.