Package com.imsl.test.example.math

Class GenMinResEx6

java.lang.Object
com.imsl.test.example.math.GenMinResEx6
All Implemented Interfaces:
GenMinRes.Function, GenMinRes.Preconditioner
public class GenMinResEx6 extends Object implements GenMinRes.Preconditioner

Solves the Poisson equation using the second Householder implementation and preconditioning.

The coefficient matrix in this example corresponds to the five-point discretization of the 2-d Poisson equation with the Dirichlet boundary condition. Assuming the natural ordering of the unknowns, and moving all boundary terms to the right hand side, we obtain a block tridiagonal matrix. (Consider the tridiagonal matrix \(T\) which has the value 4.0 down the main diagonal and -1.0 along the upper and lower co-diagonals. Then the coefficient matrix is the block tridiagonal matrix consisting of \(T\)'s down the main diagonal and \(-I\), the identity matrix, along the upper and lower co-diagonals.)

Discretizing on a 20 x 20 grid implies that the coefficient matrix is 400 x 400. In the solution, the second Householder implementation is selected and we choose to update the residual vector by direct evaluation.

Preconditioning is used with the preconditioning matrix being a diagonal matrix with 4.0 down the main diagonal and -1.0 along the upper and lower co-diagonals. This preconditioner method solves this tridiagonal matrix.

See Also:

  • Constructor Details

  • Method Details

    • amultp

      public void amultp(double[] p, double[] z)
      Obtains the multiplication of the matrix a and the input p. The result is returned in z.
      Specified by:
      amultp in interface GenMinRes.Function
      Parameters:
      p - a double array with p.length=a[0].length
      z - a double array

    • preconditioner

      public void preconditioner(double[] r, double[] z)
      Solve the tridiagonal preconditioning matrix problem for z.
      Specified by:
      preconditioner in interface GenMinRes.Preconditioner
      Parameters:
      r - an input double array of length n generated during the implementation of the solve method.
      z - an output double array of length n.

    • main

      public static void main(String[] args) throws Exception
      Throws:
      Exception