com.imsl.test.example.math

Class GenMinResEx5

java.lang.Object

com.imsl.test.example.math.GenMinResEx5

All Implemented Interfaces:

GenMinRes.Function

public class GenMinResEx5
extends Object
implements GenMinRes.Function

Solves the Poisson equation using the second Householder implementation.

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.

See Also:

Code, Output

Constructor Summary

Constructors

Constructor and Description
GenMinResEx5()

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)

Methods inherited from class java.lang.Object

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

Constructor Detail

GenMinResEx5

public GenMinResEx5()

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

main

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

Throws:

Exception