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:

Code, Output

Constructor Summary

Constructors

Constructor and Description
GenMinResEx6(int n)

Method Summary

Modifier and Type	Method and Description
void	amultp(double[] p, double[] z) Obtains the multiplication of the matrix a and the input p.
static void	main(String[] args)
void	preconditioner(double[] r, double[] z) Solve the tridiagonal preconditioning matrix problem for z.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GenMinResEx6

public GenMinResEx6(int n)
             throws Exception

Throws:

Exception

Method Detail

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