com.imsl.test.example.math

Class ConjugateGradientEx1

java.lang.Object

com.imsl.test.example.math.ConjugateGradientEx1

All Implemented Interfaces:

ConjugateGradient.Function

public class ConjugateGradientEx1
extends Object
implements ConjugateGradient.Function

Solves a positive definite linear system using the conjugate gradient method.

The solution to a positive definite linear system is found. The coefficient matrix is stored as a full matrix. The system is \(Ax = b\) where $$ A=\begin{bmatrix} 1.0 & -3.0 & 2.0 \\ -3.0 & 10.0 & -5.0 \\ 2.0 & -5.0 & 6.0 \end{bmatrix} $$

and \( b = (27.0, -78.0, 64.0)^T\)

See Also:

Code, Output

Constructor Summary

Constructors

Constructor and Description
ConjugateGradientEx1()

Method Summary

Modifier and Type	Method and Description
void	amultp(double[] p, double[] z) A user-supplied function which computes z=Ap.
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

ConjugateGradientEx1

public ConjugateGradientEx1()

Method Detail

amultp

public void amultp(double[] p,
                   double[] z)

Description copied from interface: ConjugateGradient.Function

A user-supplied function which computes z=Ap.

Specified by:

amultp in interface ConjugateGradient.Function

Parameters:

p - an input double vector of length dimension of A.

z - an output double vector containing the matrix-vector product Ap.

main

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

Throws:

Exception