• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.376-386
• /
• 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
• /
• 제40권3호
• /
• pp.329-339
• /
• 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.

• 대한수학회보
• /
• 제40권3호
• /
• pp.425-435
• /
• 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
• /
• 제3권3호
• /
• pp.75-81
• /
• 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
• /
• 제19권1_2호
• /
• pp.427-438
• /
• 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.

• 대한수학회논문집
• /
• 제21권2호
• /
• pp.397-407
• /
• 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.

• 한국통신학회논문지
• /
• 제14권4호
• /
• pp.374-387
• /
• 1989

대칭행렬식계산에 의한 2원 BCH부호의 복호방법을 제안한다. 이 복호법은 오류위치번호와 미지주 X의 판별식인 대칭행렬식을 오류위치다항식으로 이용한 것으로 오류위치다항식 계수를 구하는 방법으로 기존의 어느 방법보다 간단하고 복호기 구성도 간단하다. 본 논문에서는 대칭행렬을 이용한 복호알고리즘을 설명하고 일반적인 복호기를 구성한 후 시뮬레이션을 통해 그 정당함을 입증하였으며 (63.45)BCH 부호에 적용하여 복호기를 구성하였다. 그리고 Peterson-Borenstein -Zierler 알고리즘과 유한체 연산의 횟수와 하드웨어의 복잡도를 비교하여 본 복호방법이 효율적임을 보였다.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.45-57
• /
• 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
• /
• 제12권4호
• /
• pp.591-611
• /
• 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.

• 한국컴퓨터정보학회논문지
• /
• 제19권4호
• /
• pp.91-99
• /
• 2014

본 논문은 2차 할당 문제의 최적 해를 찾을 수 있는 휴리스틱 다항시간 알고리즘을 제안하였다. 일반적으로 선형 할당 문제의 최적 해는 헝가리안 알고리즘으로 구한다. 그러나 2차 할당문제의 최적 해를 찾는 알고리즘은 제안되지 않고 있다. 제안된 알고리즘은 거리행렬의 단위거리로부터 그리드 형태의 배치를 찾아내고, 이 형태에 맞도록 흐름량 행렬의 최대 값부터 내림차순으로 최대흐름을 최소 거리에 배치하는 최대흐름/최소거리 기법을 적용하였다. 제안된 알고리즘을 다양한 그리드형 2차 할당문제에 적용한 결과 2차 할당문제의 해를 다항시간에 구할 수 있는 알고리즘이 존재할 가능성을 보였다.