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Features:
 - Gauss-Seidel Convergence Rate Analyzer (16, 17, 18) Bug Fixes/Re-organization: - Off-diagonal Jacobi Iteration Elements (52) Samples: - SOR Relaxation Parameter Convergence #1 (1, 2, 3) - SOR Relaxation Parameter Convergence #2 (4, 5, 6) - SOR Relaxation Parameter Convergence #3 (7, 8, 9) - SOR Relaxation Parameter Convergence #4 (10, 11, 12) - SOR Relaxation Parameter Convergence #5 (13, 14, 15) - SOR Relaxation Parameter Convergence #6 (19, 20, 21) - SOR Matrix Conditioning Checks #1 (22, 23, 24) - SOR Matrix Conditioning Checks #2 (25, 26, 27) - SOR Matrix Conditioning Checks #3 (28, 29, 30) - SOR Matrix Conditioning Checks #4 (31, 32, 33) - SOR Matrix Conditioning Checks #5 (34, 35, 36) - SOR Matrix Conditioning Checks #6 (37, 38, 39) - SOR DUL Matrix Decomposition #1 (40, 41, 42) - SOR DUL Matrix Decomposition #2 (43, 44, 45) - SOR DUL Matrix Decomposition #3 (46, 47, 48) - SOR DUL Matrix Decomposition #4 (49, 50, 51) IdeaDRIP: - Crank-Nicolson Method (53-60) - Crank-Nicolson Method - Principle (61-74) - Crank-Nicolson Method - Example: 1D Diffusion (75-84) - Crank-Nicolson Method - Example: 1D Diffusion with Advection for Steady Flow, with Multiple Channel Connections (85-120)
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6 files changed

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‎ReleaseNotes/01_11_2024.txt

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Features:
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- Gauss-Seidel Convergence Rate Analyzer (16, 17, 18)
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Bug Fixes/Re-organization:
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- Off-diagonal Jacobi Iteration Elements (52)
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Samples:
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- SOR Relaxation Parameter Convergence #1 (1, 2, 3)
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- SOR Relaxation Parameter Convergence #2 (4, 5, 6)
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- SOR Relaxation Parameter Convergence #3 (7, 8, 9)
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- SOR Relaxation Parameter Convergence #4 (10, 11, 12)
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- SOR Relaxation Parameter Convergence #5 (13, 14, 15)
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- SOR Relaxation Parameter Convergence #6 (19, 20, 21)
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- SOR Matrix Conditioning Checks #1 (22, 23, 24)
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- SOR Matrix Conditioning Checks #2 (25, 26, 27)
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- SOR Matrix Conditioning Checks #3 (28, 29, 30)
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- SOR Matrix Conditioning Checks #4 (31, 32, 33)
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- SOR Matrix Conditioning Checks #5 (34, 35, 36)
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- SOR Matrix Conditioning Checks #6 (37, 38, 39)
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- SOR DUL Matrix Decomposition #1 (40, 41, 42)
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- SOR DUL Matrix Decomposition #2 (43, 44, 45)
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- SOR DUL Matrix Decomposition #3 (46, 47, 48)
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- SOR DUL Matrix Decomposition #4 (49, 50, 51)
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IdeaDRIP:
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- Crank-Nicolson Method (53-60)
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- Crank-Nicolson Method - Principle (61-74)
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- Crank-Nicolson Method - Example: 1D Diffusion (75-84)
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- Crank-Nicolson Method - Example: 1D Diffusion with Advection for Steady Flow, with Multiple Channel Connections (85-120)

‎src/main/java/org/drip/numerical/iterativesolver/SuccessiveOverRelaxationConvergenceAnalyzer.java

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@@ -287,6 +287,18 @@ public double optimalRelaxationParameter()
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return 1. + spectralRadiusTransformer * spectralRadiusTransformer;
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}
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/**
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* Estimate the Gauss-Seidel Convergence Rate from the Relaxation Parameter and the Jacobi Iteration
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* Matrix Spectral Radius
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*
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* @return Gauss-Seidel Convergence Rate
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*/
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public double gaussSeidelRate()
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{
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return _jacobiIterationMatrixSpectralRadius * _jacobiIterationMatrixSpectralRadius;
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}
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/**
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* Estimate the Convergence Rate from the Relaxation Parameter and the Jacobi Iteration Matrix Spectral
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* Radius
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public double rate()
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{
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if (SuccessiveOverRelaxationIteratorSetting.RELAXATION_PARAMETER_GAUSS_SEIDEL == _relaxationParameter)
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{
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return _jacobiIterationMatrixSpectralRadius * _jacobiIterationMatrixSpectralRadius;
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}
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double optimalRelaxationParameter = optimalRelaxationParameter();
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if (_relaxationParameter <= optimalRelaxationParameter) {
@@ -322,7 +329,7 @@ public double rate()
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* @return Convergence Rate corresponding to Optimal Relaxation Parameter
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*/
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public double optimalRelaxationParameterRate()
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public double optimalRate()
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{
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double sqrtOneMinusMuSquared =
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Math.sqrt (1. - _jacobiIterationMatrixSpectralRadius * _jacobiIterationMatrixSpectralRadius);

‎src/main/java/org/drip/numerical/linearalgebra/Matrix.java

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@@ -1342,7 +1342,7 @@ public static final double[][] JacobiIteration (
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for (int i = 0; i < size; ++i) {
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for (int j = 0; j < size; ++j) {
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jacobiIterationMatrix[i][j] = i == j ? 0. : 1. - squareMatrix[i][j];
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jacobiIterationMatrix[i][j] = i == j ? 0. : squareMatrix[i][j];
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}
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}
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‎src/main/java/org/drip/sample/sor/DULDecomposition.java

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package org.drip.sample.sor;
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import org.drip.numerical.common.NumberUtil;
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import org.drip.numerical.linearalgebra.Matrix;
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import org.drip.service.env.EnvManager;
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/*
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* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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*/
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/*!
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* Copyright (C) 2025 Lakshmi Krishnamurthy
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*
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* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
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* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
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* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
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* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
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* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
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* graph builder/navigator, and computational support.
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*
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* https://lakshmidrip.github.io/DROP/
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*
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* DROP is composed of three modules:
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*
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* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
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* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
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* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
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*
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* DROP Product Core implements libraries for the following:
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* - Fixed Income Analytics
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* - Loan Analytics
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* - Transaction Cost Analytics
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*
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* DROP Portfolio Core implements libraries for the following:
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* - Asset Allocation Analytics
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* - Asset Liability Management Analytics
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* - Capital Estimation Analytics
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* - Exposure Analytics
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* - Margin Analytics
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* - XVA Analytics
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*
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* DROP Computational Core implements libraries for the following:
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* - Algorithm Support
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* - Computation Support
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* - Function Analysis
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* - Graph Algorithm
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* - Model Validation
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* - Numerical Analysis
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* - Numerical Optimizer
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* - Spline Builder
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* - Statistical Learning
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*
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* Documentation for DROP is Spread Over:
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*
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* - Main => https://lakshmidrip.github.io/DROP/
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* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
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* - GitHub => https://github.com/lakshmiDRIP/DROP
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* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
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* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
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* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
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* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
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* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
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* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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*
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* You may obtain a copy of the License at
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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*
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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/**
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* <i>DULDecomposition</i> demonstrates the Decomposition of a Square Matrix into Diagonal, Lower, and Upper
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* Triangular Matrices. The References are:
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*
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* <br><br>
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* <ul>
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* <li>
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* Greenbaum, A. (1997): <i>Iterative Methods for Solving Linear Systems</i> <b>Society for
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* Industrial and Applied Mathematics</b> Philadelphia, PA
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* </li>
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* <li>
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* Hackbusch, W. (2016): <i>Iterative Solution of Large Sparse Systems of Equations</i>
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* <b>Spring-Verlag</b> Berlin, Germany
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* </li>
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* <li>
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* Wikipedia (2023): Symmetric Successive Over-Relaxation
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* https://en.wikipedia.org/wiki/Symmetric_successive_over-relaxation
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* </li>
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* <li>
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* Wikipedia (2024): Successive Over-Relaxation
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* https://en.wikipedia.org/wiki/Successive_over-relaxation
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* </li>
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* <li>
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* Young, D. M. (1950): <i>Iterative methods for solving partial difference equations of elliptical
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* type</i> <b>Harvard University</b> Cambridge, MA
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* </li>
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* </ul>
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*
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* <br><br>
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* <ul>
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* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
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* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
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* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
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* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/sor/README.md">Successive Over-relaxation Customization/Usage</a></li>
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* </ul>
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* <br><br>
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*
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* @author Lakshmi Krishnamurthy
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*/
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public class DULDecomposition
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{
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/**
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* Entry Point
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*
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* @param argumentArray Command Line Argument Array
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*
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* @throws Exception Thrown on Error/Exception Situation
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*/
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public static final void main (
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final String[] argumentArray)
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throws Exception
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{
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EnvManager.InitEnv (
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""
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);
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double[][] squareMatrix = new double[][] {
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{ 4., -1., -6., 0.},
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{-5., -4., 10., 8.},
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{ 0., 9., 4., -2.},
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{ 1., 0., -7., 5.},
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};
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println ("\t| JACOBI ITERATION MATRIX ");
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System.out.println ("\t|----------------------------------------------------------------------");
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NumberUtil.Print2DArrayPair (
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"\t| SQUARE",
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" JACOBI ITERATION",
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squareMatrix,
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Matrix.JacobiIteration (squareMatrix),
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false
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);
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println();
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System.out.println();
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println ("\t| DIAGONALIZED MATRIX ");
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System.out.println ("\t|----------------------------------------------------------------------");
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NumberUtil.Print2DArrayPair (
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"\t| SQUARE",
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" DIAGONAL",
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squareMatrix,
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Matrix.Diagonal (squareMatrix),
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false
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);
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println();
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System.out.println();
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println ("\t| STRICTLY LOWER TRIANGULAR MATRIX ");
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System.out.println ("\t|----------------------------------------------------------------------");
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NumberUtil.Print2DArrayPair (
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"\t| SQUARE",
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" LOWER TRIANGULAR",
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squareMatrix,
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Matrix.StrictlyLowerTriangular (squareMatrix),
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false
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);
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println();
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System.out.println();
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System.out.println ("\t|----------------------------------------------------------------------");
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System.out.println ("\t| STRICTLY UPPER TRIANGULAR MATRIX ");
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System.out.println ("\t|----------------------------------------------------------------------");
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NumberUtil.Print2DArrayPair (
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"\t| SQUARE",
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" UPPER TRIANGULAR",
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squareMatrix,
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Matrix.StrictlyUpperTriangular (squareMatrix),
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false
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);
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System.out.println ("\t|----------------------------------------------------------------------");
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EnvManager.TerminateEnv();
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}
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}

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