• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• 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
• /
• v.17 no.3
• /
• pp.462-472
• /
• 2021

With an increase in the scale of recommender systems, users' rating data tend to be extremely sparse. Some methods have been utilized to alleviate this problem; nevertheless, it has not been satisfactorily solved yet. Therefore, we propose an effective pre-rating method based on users' dichotomous preferences and average ratings fusion. First, based on a user-item ratings matrix, a new user-item preference matrix was constructed to analyze and model user preferences. The items were then divided into two categories based on a parameterized dynamic threshold. The missing ratings for items that the user was not interested in were directly filled with the lowest user rating; otherwise, fusion ratings were utilized to fill the missing ratings. Further, an optimized parameter λ was introduced to adjust their weights. Finally, we verified our method on a standard dataset. The experimental results show that our method can effectively reduce the prediction error and improve the recommendation quality. As for its application, our method is effective, but not complicated.

• Kyungpook Mathematical Journal
• /
• v.43 no.4
• /
• pp.605-616
• /
• 2003

In this paper, some rank equalities related to generalized inverses $A^{(2)}_{T,S}$ of a matrix are presented. As applications, a variety of rank equalities related to the M-P inverse, the Drazin inverse, the group inverse, the weighted M-P inverse, the Bott-Duffin inverse and the generalized Bott-Duffin inverse are established.

• Journal of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1139-1150
• /
• 2009

We obtain necessary and sufficient conditions for $2{\tims}2$ block operator valued matrices to be Moore-Penrose (MP) invertible and give new representations of such MP inverses in terms of the individual blocks.

• Journal of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.941-953
• /
• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Honam Mathematical Journal
• /
• v.29 no.1
• /
• pp.75-81
• /
• 2007

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the normal distribution using its Fisher's matrix is defined. The Riemannian curvature and J-divergence to parameter space are calculated.

• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1011-1020
• /
• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• Smart Structures and Systems
• /
• v.19 no.2
• /
• pp.203-211
• /
• 2017

This paper provides a numerical solution for multiple confocal elliptic dissimilar cylinders. In the problem, the inner elliptic notch is under the traction free condition. The medium is composed of many confocal elliptic dissimilar cylinders. The transfer matrix method is used to study the continuity condition for the stress and displacement along the interfaces. Two cases, or the infinite matrix case and the finite matrix case, are studied in this paper. In the former case, the remote tension is applied in y- direction. In the latter case, the normal loading is applied along the exterior elliptic contour. For two cases, several numerical results are provided.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.913-920
• /
• 2018

Let R be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over R is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices.

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