• 제목/요약/키워드: General linear methods

검색결과 540건 처리시간 0.024초

FSAL MONO-IMPLICIT NORDSIECK GENERAL LINEAR METHODS WITH INHERENT RUNGE-KUTTA STABILITY FOR DAES

  • OLATUNJI, P.O.;IKHILE, M.N.O.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제25권4호
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    • pp.262-295
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    • 2021
  • This paper introduces mono-implicit general linear methods, a special class of general linear methods, which are implicit in the output solution for the numerical integration of differential algebraic equations. We show how L-stable inherent Runge-Kutta members can be derived. The procedures for implementation have been discussed. The numerical test on the problem considered shows that the methods have improved accuracy when compared to RADAU IIA and the results from MATLAB ode15s, which have been taken as our reference solution.

Normal Mixture Model with General Linear Regressive Restriction: Applied to Microarray Gene Clustering

  • Kim, Seung-Gu
    • Communications for Statistical Applications and Methods
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    • 제14권1호
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    • pp.205-213
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    • 2007
  • In this paper, the normal mixture model subjected to general linear restriction for component-means based on linear regression is proposed, and its fitting method by EM algorithm and Lagrange multiplier is provided. This model is applied to gene clustering of microarray expression data, which demonstrates it has very good performances for real data set. This model also allows to obtain the clusters that an analyst wants to find out in the fashion that the hypothesis for component-means is represented by the design matrices and the linear restriction matrices.

PRECONDITIONED AOR ITERATIVE METHODS FOR SOLVING MULTI-LINEAR SYSTEMS WITH 𝓜-TENSOR

  • QI, MENG;SHAO, XINHUI
    • Journal of applied mathematics & informatics
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    • 제39권3_4호
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    • pp.587-600
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    • 2021
  • Some problems in engineering and science can be equivalently transformed into solving multi-linear systems. In this paper, we propose two preconditioned AOR iteration methods to solve multi-linear systems with -tensor. Based on these methods, the general conditions of preconditioners are given. We give the convergence theorem and comparison theorem of the two methods. The results of numerical examples show that methods we propose are more effective.

A General Mixed Linear Model with Left-Censored Data

  • Ha, Il-Do
    • Communications for Statistical Applications and Methods
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    • 제15권6호
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    • pp.969-976
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    • 2008
  • Mixed linear models have been widely used in various correlated data including multivariate survival data. In this paper we extend hierarchical-likelihood(h-likelihood) approach for mixed linear models with right censored data to that for left censored data. We also allow a general random-effect structure and propose the estimation procedure. The proposed method is illustrated using a numerical data set and is also compared with marginal likelihood method.

Matrix Formation in Univariate and Multivariate General Linear Models

  • Arwa A. Alkhalaf
    • International Journal of Computer Science & Network Security
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    • 제24권4호
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    • pp.44-50
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    • 2024
  • This paper offers an overview of matrix formation and calculation techniques within the framework of General Linear Models (GLMs). It takes a sequential approach, beginning with a detailed exploration of matrix formation and calculation methods in regression analysis and univariate analysis of variance (ANOVA). Subsequently, it extends the discussion to cover multivariate analysis of variance (MANOVA). The primary objective of this study was to provide a clear and accessible explanation of the underlying matrices that play a crucial role in GLMs. Through linking, essentially different statistical methods, by fundamental principles and algebraic foundations that underpin the GLM estimation. Insights presented here aim to assist researchers, statisticians, and data analysts in enhancing their understanding of GLMs and their practical implementation in diverse research domains. This paper contributes to a better comprehension of the matrix-based techniques that can be extended to GLMs.

The General Linear Test in the Ridge Regression

  • Bae, Whasoo;Kim, Minji;Kim, Choongrak
    • Communications for Statistical Applications and Methods
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    • 제21권4호
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    • pp.297-307
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    • 2014
  • We derive a test statistic for the general linear test in the ridge regression model. The exact distribution for the test statistic is too difficult to derive; therefore, we suggest an approximate reference distribution. We use numerical studies to verify that the suggested distribution for the test statistic is appropriate. A asymptotic result for the test statistic also is considered.

2차 하수를 이용한 비 선형 패턴인식 알고리즘 구축 (Construction of A Nonlinear Classification Algorithm Using Quadratic Functions)

  • 김락상
    • 한국경영과학회지
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    • 제25권4호
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    • pp.55-65
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    • 2000
  • This paper presents a linear programming based algorithm for pattern classification. Pattern classification is being considered to be critical in the area of artificial intelligence and business applications. Previous methods employing linear programming have been aimed at two-group discrimination with one or more linear discriminant functions. Therefore, there are some limitations in applying available linear programming formulations directly to general multi-class classification problems. The algorithm proposed in this manuscript is based on quadratic or polynomial discriminant functions, which allow more flexibility in covering the class regions in the N-dimensional space. The proposed algorithm is compared with other competitive methods of pattern classification in experimental results and is shown to be competitive enough for a general purpose classifier.

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수정된 Karmarkar 기법과 이의 효율성

  • 정성진;이창훈
    • 대한산업공학회지
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    • 제13권1호
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    • pp.53-60
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    • 1987
  • Karmakar suggested two methods to transform the general linear programming into his specially structured linear programming problem. We show that there are bad cases that cause difficulties in the use of Karmakar's methods. We also develop a new transformation method which can handle those difficulties.

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Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances

  • Schueller, G.I.
    • Structural Engineering and Mechanics
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    • 제32권1호
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    • pp.1-20
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    • 2009
  • The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis. Presently available procedures to describe uncertainties in load and resistance within a suitable mathematical framework are shortly addressed. Monte Carlo methods are proposed for studying the variability in the structural properties and for their propagation to the response. The general applicability and versatility of Monte Carlo Simulation is demonstrated in the context with computational models that have been developed for deterministic structural analysis. After discussing Direct Monte Carlo Simulation for the assessment of the response variability, some recently developed advanced Monte Carlo methods applied for reliability assessment are described, such as Importance Sampling for linear uncertain structures subjected to Gaussian loading, Line Sampling in linear dynamics and Subset simulation. The numerical example demonstrates the applicability of Line Sampling to general linear uncertain FE systems under Gaussian distributed excitation.

공간 데이터와 시계열 데이터로부터 유도된 공분산행렬을 결합한 강수량 결측값 추정 모형 (Development of a Model Combining Covariance Matrices Derived from Spatial and Temporal Data to Estimate Missing Rainfall Data)

  • 성찬용
    • 한국환경과학회지
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    • 제22권3호
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    • pp.303-308
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    • 2013
  • This paper proposed a new method for estimating missing values in time series rainfall data. The proposed method integrated the two most widely used estimation methods, general linear model(GLM) and ordinary kriging(OK), by taking a weighted average of covariance matrices derived from each of the two methods. The proposed method was cross-validated using daily rainfall data at thirteen rain gauges in the Hyeong-san River basin. The goodness-of-fit of the proposed method was higher than those of GLM and OK, which can be attributed to the weighting algorithm that was designed to minimize errors caused by violations of assumptions of the two existing methods. This result suggests that the proposed method is more accurate in missing values in time series rainfall data, especially in a region where the assumptions of existing methods are not met, i.e., rainfall varies by season and topography is heterogeneous.