• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.115-123
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• 1997

In this paper we present a polynomial matrix decomposition algorithm that determines a polynomial matix M(z) which satisfies the relation V(z)=M(z) for a given polynomial matrix V(z) which is paraconjugate hermitian matrix with normal rank r and is positive semidenfinite on the unit circle of z-plane. All the decomposition procedures in this proposed method are performed in the digitral domain. We also discuss how to apply the polynomial matirx decomposition in realizing MIMO LBR two-pairs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.437-447
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• 2003

We propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used fur spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR Inter and for the case of the IIR filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.545-551
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• 2008

Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\rho$(R[x]) = ($\rho$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1159-1174
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• 1996

The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.1
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• pp.35-44
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• 2004

We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.39-46
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• 2007

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form G(X)=$A_0X^m+A_1X^{m-1}+{\cdots}+A_m$ where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ real matrices. We show how the minimization methods can be used to solve the matrix polynomial G(X) and give some numerical experiments. We also compare Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version of conjugate gradient method.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.101-112
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• 2010

In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over $\mathbb{Q}$ which are not of Eisenstein type.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.275-285
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• 2013

In this paper a nonlinear matrix equation is considered which has the form $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_{m-1}X+A_m=0$$ where X is an $n{\times}n$ unknown real matrix and $A_m$, $A_{m-1}$, ${\cdots}$, $A_0$ are $n{\times}n$ matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P(X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fr$\acute{e}$echet derivative of P(X) is singular.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.113-124
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• 2010

We consider matrix polynomial which has the form $P_1(X)=A_oX^m+A_1X^{m-1}+...+A_m=0$ where X and $A_i$ are $n{\times}n$ matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation $P_1(X)$. Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton's method. Finally, we give some numerical experiments that confirm the theoretical results.