Q_SylvestKt

All Implemented Interfaces:


public final class Q_SylvestKt

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description

Field Summary

Fields
Modifier and Type	Field	Description

Constructor Summary

Constructors
Constructor	Description

Enum Constant Summary

Enum Constants
Enum Constant	Description

Method Summary

Modifier and Type	Method	Description
`final static Matrix`	`qSylvest(Matrix U, Matrix T, Matrix B)`	Solves the equation X*kron(A,I)+BX=-I using a Schur-based approach.
`final static Pair<Matrix, Matrix>`	`schurDecomposition(Matrix A)`	Performs Schur decomposition of a matrix.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
- Method Detail
  - qSylvest
```
 final static Matrix qSylvest(Matrix U, Matrix T, Matrix B)
```
    Solves the equation X*kron(A,I)+BX=-I using a Schur-based approach.
    Uses pre-computed Schur decomposition where kron(A,I)=UTU'
    
    Parameters:
    
    U - The unitary matrix from Schur decomposition
    
    T - The triangular matrix from Schur decomposition
    
    B - The matrix B in the equation
    
    Returns:
    
    Solution matrix X
  - schurDecomposition
```
 final static Pair<Matrix, Matrix> schurDecomposition(Matrix A)
```
    Performs Schur decomposition of a matrix.
    Returns a pair (U, T) where A = U * T * U' Uses eigenvalue decomposition as a fallback since direct Schur decomposition is not publicly accessible in commons-math3.
    
    Parameters:
    
    A - Input matrix
    
    Returns:
    
    Pair of (U, T) matrices