• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• East Asian mathematical journal
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• v.40 no.3
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• pp.329-339
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• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.425-435
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• 2003

In this paper, a new kind of matrices, i.e., $level-{\kappa}$ II-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Grobner basis of the ideal in the polynomial ring. Two algorithms for finding the inverses of such matrices are also presented based on the Buchberger's algorithm.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.75-81
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• 1996

Polynomial measurement error model(MEM) with one predictor is considered. It is briefly mentioned that Chan and Mak's generalized least squares estimator(GLSE) can be derived more easily if Hermite polynomial concept is applied. It is proved that GLSE derived using new procedure is equivalent to the estimator obtained from corrected score function. Finally, much simpler proof of the asymptotic behavior of GLSE than that of Chan and Mak is provided. Much simpler formula of asymptotic covariance matrix of GLSE is a part of that proof.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.4
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• pp.374-387
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• 1989

The decoding method of Binary BCH Codes using symmetric matrix is proposed in this paper. With this method, the error-locator-polynomial is composed by symmetric matrix which consists of the powers of the unknown X plus the synfromes as its elements. The symmetric matirx can also be represented in terms of the unknown X. But the each coefficients of the error-locator polynomial represents the matirx with the syndromes as its entries. By utilizing this proposed algorithm, the device for decoding circuit of the (63, 45) BCH Code for t=3 has been implemented for demonstration.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.45-57
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• 2005

An efficient algorithm for finding the inverse and the group inverse of the FLS $\gamma-circulant$ matrix is presented by Euclidean algorithm. Extension is made to compute the inverse of the FLS $\gamma-retrocirculant$ matrix by using the relationship between an FLS $\gamma-circulant$ matrix and an FLS $\gamma-retrocirculant$ matrix. Finally, some examples are given.

• Journal of Information Processing Systems
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• v.12 no.4
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• pp.591-611
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• 2016

High dimensional space is the biggest problem when classification process is carried out, because it takes longer time for computation, so that the costs involved are also expensive. In this research, the facial space generated from homogeneous and non-homogeneous polynomial was proposed to extract the facial image features. The homogeneous and non-homogeneous polynomial-based eigenspaces are the second opinion of the feature extraction of an appearance method to solve non-linear features. The kernel trick has been used to complete the matrix computation on the homogeneous and non-homogeneous polynomial. The weight and projection of the new feature space of the proposed method have been evaluated by using the three face image databases, i.e., the YALE, the ORL, and the UoB. The experimental results have produced the highest recognition rate 94.44%, 97.5%, and 94% for the YALE, ORL, and UoB, respectively. The results explain that the proposed method has produced the higher recognition than the other methods, such as the Eigenface, Fisherface, Laplacianfaces, and O-Laplacianfaces.

• Journal of the Korea Society of Computer and Information
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• v.19 no.4
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• pp.91-99
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• 2014

TThis paper suggests an heuristic polynomial time algorithm to solve the optimal solution for QAP (quadratic assignment problem). While Hungarian algorithm is most commonly used for a linear assignment, there is no polynomial time algorithm for the QAP. The proposed algorithm derives a grid type layout among unit distances of a distance matrix. And, we apply max-flow/min-distance approach to assign this grid type layout in such a descending order way that the largest flow is matched to the smallest unit distance from flow matrix. Evidences from implementation results of the proposed algorithm on various numerical grid type QAP examples show that a solution to the QAP could be obtained by a polynomial algorithm.