
On Factor Left Prime Factorization Problems for Multivariate Polynomial Matrices
This paper is concerned with factor left prime factorization problems fo...
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Factorizations for a Class of Multivariate Polynomial Matrices
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6):...
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On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
A new necessary and sufficient condition for the existence of minor left...
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Factoring Perfect Reconstruction Filter Banks into Causal Lifting Matrices: A Diophantine Approach
The theory of linear Diophantine equations in two unknowns over polynomi...
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On the computational equivalence of coNP refutations of a matrix being a Pmatrix
A Pmatrix is a square matrix X such that all principal submatrices of X...
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Efficient Determination of Equivalence for Encrypted Data
Secure computation of equivalence has fundamental application in many di...
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Equivalence theorems for compound design problems with application in mixed models
In the present paper we consider design criteria which depend on several...
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New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial Matrices
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain a necessary and sufficient condition for the equivalence of a square polynomial matrix and a diagonal matrix. Based on the constructive proof of the new criteria, we give a factorization algorithm and prove the uniqueness of the factorization. We implement the algorithm on Maple, and two illustrative examples are given to show the effectiveness of the algorithm.
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