Package org.drip.numerical.iterativesolver

Class SymmetricSuccessiveOverRelaxation

java.lang.Object

org.drip.numerical.iterativesolver.SuccessiveOverRelaxation

org.drip.numerical.iterativesolver.SymmetricSuccessiveOverRelaxation

public class SymmetricSuccessiveOverRelaxation
extends SuccessiveOverRelaxation

SymmetricSuccessiveOverRelaxation implements the SSOR Linear Solution scheme. 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
SymmetricSuccessiveOverRelaxation(SuccessiveOverRelaxationIteratorSetting iteratorSetting, double[][] squareMatrix, double[] rhsArray)	SymmetricSuccessiveOverRelaxation Constructor

Method Summary

Modifier and Type	Method	Description
double[][]	preConditioner()	Compute the Pre-conditioner Matrix
double[]	preConditioningIteration(double gamma)	Solve using Pre-conditioning Iteration of the Input Square Matrix

Methods inherited from class org.drip.numerical.iterativesolver.SuccessiveOverRelaxation

diagonalMatrix, forwardSubstitution, iteratorSetting, rhsArray, squareMatrix, Standard, strictlyLowerTriangularMatrix, strictlyUpperTriangularMatrix

Methods inherited from class java.lang.Object

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

Constructor Details

SymmetricSuccessiveOverRelaxation

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

SymmetricSuccessiveOverRelaxation 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

preConditioner

public double[][] preConditioner()

Compute the Pre-conditioner Matrix

Returns:

Pre-conditioner Matrix

preConditioningIteration

public double[] preConditioningIteration(double gamma)

Solve using Pre-conditioning Iteration of the Input Square Matrix

Parameters:

gamma - Gamma

Returns:

The Solution Array