Interface Preconditioner

public interface Preconditioner
The preconditioner matrix. A preconditioner P of a matrix A is a matrix such that P-1A has a smaller condition number than A. Preconditioners are useful in iterative methods to solve a linear system A * x = b since the rate of convergence for most iterative linear solvers increases because the condition number of a matrix decreases as a result of preconditioning. Preconditioned iterative solvers typically outperform direct solvers for large, especially for sparse matrices.

The preconditioner matrix P is close to A and should be easy to solve for linear systems. The preconditioner matrix could be as simple as the trivial diagonal part of A in some cases.

  • Method Summary

    Modifier and Type
    Method
    Description
    static Preconditioner
    Jacobi(Matrix A)
    Returns a simple Jacobi preconditioner matrix that is the trivial diagonal part of A in some cases.
    void
    solve(Vector b, Vector x)
    Solve P * x = b for the preconditioner matrix P.

  • Method Details

    • solve

      void solve(Vector b, Vector x)
      Solve P * x = b for the preconditioner matrix P.
      Parameters:
      b - the right hand side of linear system.
      x - the output solution vector.

    • Jacobi

      static Preconditioner Jacobi(Matrix A)
      Returns a simple Jacobi preconditioner matrix that is the trivial diagonal part of A in some cases.
      Parameters:
      A - the matrix of linear system.
      Returns:
      the preconditioner matrix.