• Proceedings of the Korean Geotechical Society Conference
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• 1999.10a
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• pp.177-184
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• 1999

In general tile evaluation process of rock slope stability is an ambiguous system which is made up of ideas subjected to practical experience of an expert. This paper aims to propose more effective methods that helps engineers to evaluate the stability of rock slope by using RMR(Rock Mass Rating for the Geomechanics Classification) and Stereo-graphic Projection and Fuzzy Approximate Reasoning Concept. the result of this paper is that a rational evaluation of rock slope stability and countermeasures can be achieved thorough RMR. and Stereo-graphic Projection and Fuzzy Approximate Reasoning Concept.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• East Asian mathematical journal
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• v.24 no.1
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• pp.57-65
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• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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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.

• The Journal of Engineering Geology
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• v.11 no.2
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• pp.153-161
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• 2001

The quantitative evaluation of the stereo graphic projection, the limit equilibrium analysis, the finite difference analysis, the distinct element methocI is a analytical evaluation using many variables. Through the reliability analysis by the point estimation technique, uncertainty of other variables that have an effect on the stability of the rock slo~ was considered. The organized evaluation method of the approximate reasoning concept and using a fuzzy language was developed to confer and analysis the failure factors in planning and constructing the rock slope. Considering the result of the an- alysis, it was demonstrated that stability of entire sections can be evaluated through reliability analysis of point estimation technique. The results of stability evaluation by Fuzzy Approximate Reasoning is generally identical with the results of other existirw; analyses. As mentioned above, general and organized evaluation of special qualities of rock slope is possible using RMR Classification, Stereo Graphic Projection, Limit Equilibriwn Analysis, Finite Difference Analysis, Distinct Element Method, Point Estimation Technique, and Fuzzy Approximate Reasoning.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.661-667
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• 2013

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9B
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• pp.1785-1794
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• 1999

The affine projection algorithm has known t require less computational complexity than RLS but have much faster convergence than NLMS for speech-like input signals. But the affine projection algorithm is still much more computationally demanding than the LMS algorithm because it requires the matrix inversion. In this paper, we show that the affine projection algorithm can be realized with the Gram-Schmidt orthogonalizaion of input vectors. Using the derived relation, we propose an approximate but much more efficient implementation of the affine projection algorithm. Simulation results show that the proposed algorithm has the convergence speed that is comparable to the affine projection algorithm with only a slight extra calculation complexity beyond that of NLMS.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.3_4
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• pp.195-203
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• 2004

VolumePro is a real-time volume rendering hardware for consumer PCs. However it cannot be used for the applications requiring perspective projection such as virtual endoscopy since it provides only orthographic projection. Several methods have been presented to approximate perspective projection by decomposing a volume into slabs and applying successive parallel projection to thou. But it takes a lot of time since the entire region of every slab should be processed, which does not contribute to final image. In this paper, we propose an efficient perspective projection method that makes the use of several sub-volumes with cropping feature of VolumePro. It reduces the rendering time in comparison to slab-based method without image quality deterioration since it processes only the parts contained in the view frustum.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.431-440
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• 2009

In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].