OOF2: The Manual

Name

CG (ConjugateGradient) — Conjugate Gradient method for iteratively solving symmetric matrices.

Synopsis

ConjugateGradient(preconditioner,tolerance,max_iterations)

Details

  • Base class: MatrixMethod
  • Parameters:

    preconditioner
    Black magic for making the matrix more easily solvable. Type: An object of the Preconditioner class.
    tolerance
    Largest acceptable relative error in the matrix solution. Type: A real number.
    max_iterations
    Maximum number of iterations to perform. Type: Integer.

Description

The CG matrix method implements the preconditioned Conjugate Gradient method for solving linear matrix equations in AdvancedSolverMode. The matrix must be symmetric.

CG is an iterative method, meaning that it creates an approximate solution and improves it on each iteration. The iteration will cease when the relative error of the solution is less than the given tolerance. The solver will stop and report an error if the tolerance isn't satisfied within max_iterations iterations.

The preconditioner parameter specifies which Preconditioner to use, if any. Preconditioners speed the convergence of iterative methods by replacing the original matrix by something closer to the identity matrix.