Package org.drip.numerical.linearalgebra

Class SylvesterEquation

java.lang.Object
org.drip.numerical.linearalgebra.SylvesterEquation
public class SylvesterEquation
extends java.lang.Object
SylvesterEquation holds the A, B, and C components of a Sylvester Equation, which is defined by: A.X + X.B = C X is the unknown whose solution is to sought. Naturally, the sizes of A, B, and C 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
    SylvesterEquation​(R1Square squareMatrixA, R1Square squareMatrixB)
    SylvesterEquation Constructor

  • Method Summary

    Modifier and Type Method Description
    int aSize()
    Retrieve the Size of Square Matrix A
    int bSize()
    Retrieve the Size of Square Matrix B
    R1Square squareMatrixA()
    Retrieve the "A" Square Matrix
    R1Square squareMatrixB()
    Retrieve the "B" Square Matrix

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • SylvesterEquation

      public SylvesterEquation​(R1Square squareMatrixA, R1Square squareMatrixB) throws java.lang.Exception
      SylvesterEquation Constructor
      Parameters:
      squareMatrixA - "A" Square Matrix
      squareMatrixB - "B" Square Matrix
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • squareMatrixA

      public R1Square squareMatrixA()
      Retrieve the "A" Square Matrix
      Returns:
      "A" Square Matrix

    • squareMatrixB

      public R1Square squareMatrixB()
      Retrieve the "B" Square Matrix
      Returns:
      "B" Square Matrix

    • aSize

      public int aSize()
      Retrieve the Size of Square Matrix A
      Returns:
      Size of Square Matrix A

    • bSize

      public int bSize()
      Retrieve the Size of Square Matrix B
      Returns:
      Size of Square Matrix B