Package org.drip.numerical.linearsolver

Class BartelsStewartScheme

java.lang.Object
org.drip.numerical.linearsolver.BartelsStewartScheme
public class BartelsStewartScheme
extends java.lang.Object
BartelsStewartScheme implements the solution to Sylvester Equation, which is defined by: A.X + X.B = RHS X is the unknown whose solution is to sought. Naturally, the sizes of A, B, and RHS need to be consistent. The References are:

  • Bhatia, R., and P. Rosenthal (1997): How and why to solve the operator equation AX-XB=Y? Bulletin of London Mathematical Society 29 (1) 1-21
  • Dmytryshyn, A. and B. Kagstrom (2015): Coupled Sylvester-type Matrix Equation and Block Diagonalization SIAM Journal of Matrix Analysis and Applications 36 (2) 580-593
  • Gerrish, F., and A. G. B. Ward (1998): Sylvester Matrix Equation and Roth’s Removal Rule Mathematical Gazette 82 (495) 423-430
  • Wei, Q., N. Dobigeon, and J. Y. Tourneret (2015): Fast Fusion of Multi-band Images based on solving a Sylvester Equation IEEE 24 (11) 4109-4121
  • Wikipedia (2024): Sylvester Equation https://en.wikipedia.org/wiki/Sylvester_equation




Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    BartelsStewartScheme​(SylvesterEquation sylvesterEquation, double[][] rhsMatrix, boolean diagnosticsOn)
    BartelsStewartScheme Constructor

  • Method Summary

    Modifier and Type Method Description
    boolean diagnosticsOn()
    Retrieve the "RHS" Matrix
    static void main​(java.lang.String[] argumentArray)  
    double[][] rhsMatrix()
    Retrieve the Diagnostics On Flag
    void solve()  
    SylvesterEquation sylvesterEquation()
    Retrieve the Sylvester Equation Instance

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • BartelsStewartScheme

      public BartelsStewartScheme​(SylvesterEquation sylvesterEquation, double[][] rhsMatrix, boolean diagnosticsOn) throws java.lang.Exception
      BartelsStewartScheme Constructor
      Parameters:
      sylvesterEquation - Sylvester Equation Instance
      rhsMatrix - "RHS" Matrix
      diagnosticsOn - Diagnostics-on Flag
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • sylvesterEquation

      public SylvesterEquation sylvesterEquation()
      Retrieve the Sylvester Equation Instance
      Returns:
      Sylvester Equation Instance

    • diagnosticsOn

      public boolean diagnosticsOn()
      Retrieve the "RHS" Matrix
      Returns:
      "RHS" Matrix

    • rhsMatrix

      public double[][] rhsMatrix()
      Retrieve the Diagnostics On Flag
      Returns:
      Diagnostics On Flag

    • solve

      public void solve()

    • main

      public static final void main​(java.lang.String[] argumentArray) throws java.lang.Exception
      Throws:
      java.lang.Exception