• Communications for Statistical Applications and Methods
• /
• 제24권1호
• /
• pp.81-96
• /
• 2017

Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제19권2호
• /
• pp.171-188
• /
• 2015

In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.

• Nonlinear Functional Analysis and Applications
• /
• 제27권4호
• /
• pp.869-879
• /
• 2022

In this paper, we consider matrix optimization problems. We investigate augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems. Following the proofs of Eckstein [3], and Eckstein and Yao [5], we prove convergence theorems for augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems.

• 전산구조공학
• /
• 제10권1호
• /
• pp.193-200
• /
• 1997

탄성지반상의 원형탱크해석에는 여러방법이 있지만 최근에 널리 사용되는 방법은 유한요소법이다. 그러나 이 방법은 탄성지반상의 탱크해석시 많은 절점수가 필요하게 된다. 이것은 곧 많은 계산기 기억용량 및 계산시간 뿐만 아니라 노력이 필요하게 된다. 본 연구에서는 유사탄성지반보(Analogy of Beam on Elastic Foundation) 및 지반강성행렬(Foundation Stiffness Matrix)을 이용하여 축대칭하중을 받는 축대칭탱크를 뼈대 구조화 할 수 있었다. 또한 이 뼈대 구조를 유한요소로 분할하고, 각 요소 강성행렬(Stiffness Matrix)을 전달행렬(Transfer Matrix)로 전환하여 전달행렬법으로 원형탱크를 해석 할 수 있었다. 유한요소법과 전달행렬법을 탄성지반상의 원형탱크 해석에 적용한 결과 두 해석결과의 차이는 없고, 전달행렬법을 적용한 경우 최종 연립방정식수가 4개로 간략화 되었다.

• Journal of Power Electronics
• /
• 제6권1호
• /
• pp.67-72
• /
• 2006

This paper introduces two different types of AC current control methods for an indirect vector controlled induction motor using a matrix converter. The proposed methods combine the advantages of matrix converters with the advantages of the indirect vector AC current control methods. The first proposed method explains the basic idea of the hysteresis current control method for matrix converters and shows its capability and stability in comparison to the conventional method usually used for VSI. With the aid of the special configuration of the matrix converter, we also propose another current method which is modified from the first one in order to reduce both current ripple and torque ripple. Simulation results have verified the feasibility and the effectiveness of the proposed methods.

• Journal of applied mathematics & informatics
• /
• 제26권3_4호
• /
• pp.501-510
• /
• 2008

In this paper, we first provide a convergence result of the generalized two-stage splitting method for solving a linear system whose coefficient matrix is an H-matrix, and then we provide convergence results of the generalized multisplitting and two-stage multisplitting methods for both a monotone matrix and an H-matrix.

• East Asian mathematical journal
• /
• 제29권5호
• /
• pp.511-519
• /
• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• 대한수학회지
• /
• 제36권1호
• /
• pp.209-227
• /
• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• 대한수학회보
• /
• 제49권5호
• /
• pp.997-1006
• /
• 2012

In this paper, we study convergence of multisplitting methods with preweighting for solving a linear system whose coefficient matrix is an H-matrix corresponding to both the AOR multisplitting and the SSOR multisplitting. Numerical results are also provided to confirm theoretical results for the convergence of multisplitting methods with preweighting.

• 대한수학회논문집
• /
• 제34권2호
• /
• pp.657-670
• /
• 2019

In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an M-matrix. Based on the generalized Gunawardena's preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.