• 대한수학회지
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• 제52권2호
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• 제어로봇시스템학회논문지
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• 제6권5호
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• pp.339-344
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• 2000

This paper is concerned with the simplification of complex linear time-invariant systems. A simple technique is suggested using the well-known least squares method in the frequency domain. Given a high-order transfer function in the s- or z-domain, the squared-gain function corresponding to a low-order model is computed by the least squares method. Then, the low-order transfer function is obtained through the factorization. Three examples are given to illustrate the efficiency of the proposed method.

• 대한수학회지
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• 제54권2호
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• pp.613-626
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• 2017

For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.497-504
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• 2002

In meshless methods, the moving least squares approximation technique is widely used to approximate a solution space because of its useful numerical characters such as non-element approximation, easily controllable smoothness, and others. In this work, a generalized version of the moving least squares method Is introduced to enhance the approximation performance through the Information converning to the derivative of the field variable. The results of numerical tests for approximation verify the improved accuracy of the generalized meshless approximation procedure compared to the conventional moving least squares method. By using this generalized moving least squares method, meshless analysis of thin beam is carried out, and its performance is investigated.

• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.369-379
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• 1996

A study is made of approximate technique for structural reanalysis based on the force method. Perturbntion analysis of generalized least squares problem is adopted to reanalyze a damaged structure, and related results are presented.

• 전력전자학회:학술대회논문집
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• 전력전자학회 2018년도 추계학술대회
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• pp.175-176
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• 2018

This paper presents a method to estimate the parameter of permanent magnet synchronous motor using a least squares method. The approximate solution of the linear simultaneous equations is obtained by the pseudoinverse least squares method of the input current and output voltage data of the current controller. It is possible to obtain the current response of the same bandwidth to the general control target by using the Pole-zero Cancellation technique. This paper verifies the performance of the proposed method by comparing the results of estimation of parameters of different motors by simulation.

• 한국CDE학회논문집
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• 제17권4호
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• Communications for Statistical Applications and Methods
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• 제25권6호
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• pp.673-685
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• 2018

Procrustes analysis is a useful technique useful to measure, compare shape differences and estimate a mean shape for objects; however it is based on a least squares criterion and is affected by some outliers. Therefore, we propose two generalized Procrustes analysis methods based on M-estimation and least median of squares estimation that are resistant to object outliers. In addition, two algorithms are given for practical implementation. A simulation study and some examples are used to examine and compared the performances of the algorithms with the least square method. Moreover since these resistant GPA methods are available for higher dimensions, we need some methods to visualize the objects and mean shape effectively. Also since we have concentrated on resistant fitting methods without considering shape distributions, we wish to shape analysis not be sensitive to particular model.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2005년도 Proceedings of ISRS 2005
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• pp.47-51
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• 2005

Using satellite images, an optimal solution to water motion has been presented in this study. Since temperature patterns are suitable tracers in water motion, Sea Surface Temperature (SST) images of Caspian Sea taken by MODIS sensor on board Terra satellite have been used in this study. Two daily SST images with 24 hours time interval are used as input data. Computation of templates correspondence between pairs of images is crucial within motion algorithms using non-rigid body objects. Image matching methods have been applied to estimate water body motion within the two SST images. The least squares matching technique, as a flexible technique for most data matching problems, offers an optimal spatial solution for the motion estimation. The algorithm allows for simultaneous local radiometric correction and local geometrical image orientation estimation. Actually, the correspondence between the two image templates is modeled both geometrically and radiometrically. Geometric component of the model includes six geometric transformation parameters and radiometric component of the model includes two radiometric transformation parameters. Using the algorithm, the parameters are automatically corrected, optimized and assessed iteratively by the least squares algorithm. The method used in this study, has presented more efficient and robust solution compared to the traditional motion estimation schemes.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.879-886
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• 2009

본 논문에서는 시장점유율을 추정할 때 최소제곱 서포트벡터기계를 적용하여 보통최소제곱과 최소제곱 서포트벡터기계의 성능을 비교하고자 한다. 최소제곱 서포트벡터기계는 커널 함수를 사용함으로 고차원의 특징 공간에서 선형회귀로 재구성함으로 비선형 회귀문제까지도 해결할 수 있는 장점을 가지고 있다. 그래서 본 논문에서는 비모수 기법인 최소제곱 서포트벡터기계를 이용하여 시장점유율 모형을 추정하고자 한다. 최소제곱 서포트벡터기계를 기반으로 한 모형 추정은 시장점유율 유인모형을 해결하기 위한 좋은 대안이 된다. 최소제곱 서포트벡터기계의 성능을 평가하기 위해 비교 실험에서는 한국 자동차 시장에서 차량 판매량을 이용하여 브랜드별 시장점유율 모형을 추정하였다.