Dear colleagues and researchers,
The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume 22 Number 2 (June 2018 issue) has been posed on http://www.ksiam.org/archive/ Aims and scope or other information on the journal is available on the KSIAM website http://www.ksiam.org or http://www.ksiam.org/jksiam The journal is one of Korea Citation Indexed (KCI) journals since 2007. Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site http://www.ksiam.org/jksiam/
Minkyu Kwak, Editor-in-Chief
Zhiming Chen, June-Yub Lee, Tao Tang, Associate Editors-In-Chief
Jin Yeon Cho, Junseok Kim, Managing Editors
Enhanced Exemplar Based Inpainting Using Patch Ratio
Sangyeon Kim, Namsik Moon, Myungjoo Kang
In this paper, we propose a new method for template matching, patch ratio, to inpaint unknown pixels. Before this paper, many inpainting methods used sum of squared differences(SSD) or sum of absolute differences(SAD) to calculate distance between patches and it was very useful for closest patches for the template that we want to fill in. However, those methods don't consider about geometric similarity and that causes unnatural inpainting results for human visuality. Patch ratio can cover the geometric problem and moreover computational cost is less than using SSD or SAD. It is guaranteed about finding the most similar patches by Cauchy-Schwarz inequality. For ignoring unnecessary process, we compare only selected candidates by priority calculations. Exeperimental results show that the proposed algorithm is more efficent than Criminisi's one.
Finite Element Dual Singular Function Methods for Helmholtz and Heat Equations
Deok-Kyu Jang, Jae-Hong Pyo
The dual singular function method(DSFM) is a numerical algorithm to get opti- mal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman- Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.
A Modified Extended Kalman Filter Method for Multi-Layered Neural Network Training
Kyungsup Kim, Yoojae Won
This paper discusses extended Kalman filter method for solving learning problems of multilayered neural networks. A lot of learning algorithms for deep layered network are sincerely suffered from complex computation and slow convergence because of a very large number of free parameters. We consider an efficient learning algorithm for deep neural network. Extended Kalman filter method is applied to parameter estimation of neural network to improve convergence and computation complexity. We discuss how an efficient algorithm should be developed for neural network learning by using Extended Kalman filter.
Combined Laplace Transform with Analytical Methods for Solving Volterra Integral Equations with a Convolution Kernel
Fawziah Al-saar, Kirtiwant Ghadle
In this article, a homotopy perturbation transform method (HPTM) and a combined between Laplace transform and Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.