Constructive Algorithm to Vectorize P ⊗ P Product for Symmetric Matrix P

A constructive algorithm to compute elimination and duplication matrices for the operation of vectorization when is proposed. The matrix , obtained according to such algorithm, allows one to form a vector that contains only unique elements of the mentioned Kronecker product. In its turn, the matrix...

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Vydáno v:Computational mathematics and mathematical physics Ročník 63; číslo 9; s. 1559 - 1570
Hlavní autoři: Glushchenko, A. I., Lastochkin, K. A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.09.2023
Springer Nature B.V
Témata:
Algorithms
Computational Mathematics and Numerical Analysis
Control theory
Controllers
General Numerical Methods
Mathematics
Mathematics and Statistics
Matrix algebra
Parameter identification
Parameterization
Riccati equation
Symmetry
vectorization
matrix unique elements
dimensionality reduction
elimination matrix
overparameterization
duplication matrix
Kronecker product
Riccati equation
ISSN:0965-5425, 1555-6662
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Shrnutí:A constructive algorithm to compute elimination and duplication matrices for the operation of vectorization when is proposed. The matrix , obtained according to such algorithm, allows one to form a vector that contains only unique elements of the mentioned Kronecker product. In its turn, the matrix is for the inverse transformation. A software implementation of the procedure to compute the matrices and is developed. On the basis of the mentioned results, a new operation is defined for in case and its properties are studied. The difference and advantages of the developed operation in comparison with the known ones and ( ) in case of vectorization of when are demonstrated. Using parameterization of the algebraic Riccati equation as an example, the efficiency of the operation to reduce overparameterization of the unknown parameter identification problem is shown.
Bibliografie:ObjectType-Article-1
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523090099