Package org.drip.numerical.iterativesolver

Class SuccessiveOverRelaxation

java.lang.Object

org.drip.numerical.iterativesolver.SuccessiveOverRelaxation

Direct Known Subclasses:

SymmetricSuccessiveOverRelaxation

public class SuccessiveOverRelaxation
extends java.lang.Object

SuccessiveOverRelaxation implements the SOR Linear Solution schemes. The References are:

• Greenbaum, A. (1997): Iterative Methods for Solving Linear Systems Society for Industrial and Applied Mathematics Philadelphia, PA
• Hackbusch, W. (2016): Iterative Solution of Large Sparse Systems of Equations Spring-Verlag Berlin, Germany
• Wikipedia (2023): Symmetric Successive Over-Relaxation https://en.wikipedia.org/wiki/Symmetric_successive_over-relaxation
• Wikipedia (2024): Successive Over-Relaxation https://en.wikipedia.org/wiki/Successive_over-relaxation
• Young, D. M. (1950): Iterative methods for solving partial difference equations of elliptical type Harvard University Cambridge, MA

It provides the following functionality:

• Construct the R¹ To R¹ Bessel First Kind Frobenius Summation Series

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Linear System Iterative Solver Schemes

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
SuccessiveOverRelaxation(SuccessiveOverRelaxationIteratorSetting iteratorSetting, double[][] squareMatrix, double[] rhsArray)	SuccessiveOverRelaxation Constructor

Method Summary

Modifier and Type	Method	Description
double[][]	diagonalMatrix()	Retrieve the Diagonal Matrix
double[]	forwardSubstitution()	Solve using Forward Substitution
SuccessiveOverRelaxationIteratorSetting	iteratorSetting()	Retrieve the Successive Over Relaxation Iterator Setting
double[]	rhsArray()	Retrieve the RHS Array
double[][]	squareMatrix()	Retrieve the Square Matrix
static SuccessiveOverRelaxation	Standard(double[][] squareMatrix, double[] rhsArray)	Construct an Instance of SuccessiveOverRelaxation using the Standard Solver Settings
double[][]	strictlyLowerTriangularMatrix()	Retrieve the Strictly Lower Triangular Matrix
double[][]	strictlyUpperTriangularMatrix()	Retrieve the Strictly Upper Triangular Matrix

Methods inherited from class java.lang.Object

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

Constructor Details

SuccessiveOverRelaxation

public SuccessiveOverRelaxation(SuccessiveOverRelaxationIteratorSetting iteratorSetting,
double[][] squareMatrix,
double[] rhsArray)
                         throws java.lang.Exception

SuccessiveOverRelaxation Constructor

Parameters:

iteratorSetting - Successive Over-Relaxation Iterator Setting

squareMatrix - Square Matrix

rhsArray - RHS Array

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Standard

public static final SuccessiveOverRelaxation Standard(double[][] squareMatrix,
double[] rhsArray)

Construct an Instance of SuccessiveOverRelaxation using the Standard Solver Settings

Parameters:

squareMatrix - Square Matrix

rhsArray - RHS Array

Returns:

Instance of SuccessiveOverRelaxation

squareMatrix

public double[][] squareMatrix()

Retrieve the Square Matrix

Returns:

Square Matrix

diagonalMatrix

public double[][] diagonalMatrix()

Retrieve the Diagonal Matrix

Returns:

Diagonal Matrix

strictlyLowerTriangularMatrix

public double[][] strictlyLowerTriangularMatrix()

Retrieve the Strictly Lower Triangular Matrix

Returns:

Strictly Lower Triangular Matrix

strictlyUpperTriangularMatrix

public double[][] strictlyUpperTriangularMatrix()

Retrieve the Strictly Upper Triangular Matrix

Returns:

Strictly Upper Triangular Matrix

rhsArray

public double[] rhsArray()

Retrieve the RHS Array

Returns:

RHS Array

iteratorSetting

public SuccessiveOverRelaxationIteratorSetting iteratorSetting()

Retrieve the Successive Over Relaxation Iterator Setting

Returns:

Successive Over Relaxation Iterator Setting

forwardSubstitution

public double[] forwardSubstitution()

Solve using Forward Substitution

Returns:

The Solution Array