• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.507-528
• /
• 2022

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

• The Korean Journal of Applied Statistics
• /
• v.28 no.2
• /
• pp.281-288
• /
• 2015

In this paper, we study an approximate procedure to evaluate a penalized maximum likelihood estimator (MLE) for a mixed effects model. The procedure approximates the Hessian matrix of the penalized MLE with a structured sparse matrix or an arrowhead type matrix to speed its computation. In this paper, we numerically investigate the gain in computation time as well as approximation error from the considered approximation procedure.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
• /
• 2010.06a
• /
• pp.298-302
• /
• 2010

This study proposes a differential method to analyze the properties of the topographic surface driven from lidar imagery. Although airborne lidar imagery provides elevation information rapidly, a sequence of extraction processes are needed to acquire semantic information about objects such as terrain, roads, trees, vegetation, and buildings. For the processes, the properties present in a given lidar data need to be analyzed. In order to investigate the geometric characteristics of the surface, this study employs eigenvalues of the Hessian matrix. For experiments, a lidar image containing university campus buildings with the point density of about 1 meter was processed and the results show that the approach is effective to obtain the properties of each land object Surface.

• Journal of Biomedical Engineering Research
• /
• v.36 no.4
• /
• pp.79-85
• /
• 2015

The purpose of this study is to develop an automatic algorithm for vessel segmentation in X-Ray angiogram using Random Forest (RF). The proposed algorithm is composed of the following steps: First, the multiscale hessian-based filtering is performed in order to enhance the vessel structure. Second, eigenvalues and eigenvectors of hessian matrix are used to learn the RF classifier as feature vectors. Finally, we can get the result through the trained RF. We evaluated the similarity between the result of proposed algorithm and the manual segmentation using 349 frames, and compared with the results of the following two methods: Frangi et al. and Krissian et al. According to the experimental results, the proposed algorithm showed high similarity compared to other two methods.

• Journal of the Korean earth science society
• /
• v.37 no.5
• /
• pp.277-285
• /
• 2016

We introduce a depth scaling strategy to improve the accuracy of frequency-domain elastic full waveform inversion (FWI) using the new pseudo-Hessian matrix for seismic data without low-frequency components. The depth scaling strategy is based on the fact that the damping factor in the Levenberg-Marquardt method controls the energy concentration in the gradient. In other words, a large damping factor makes the Levenberg-Marquardt method similar to the steepest-descent method, by which shallow structures are mainly recovered. With a small damping factor, the Levenberg-Marquardt method becomes similar to the Gauss-Newton methods by which we can resolve deep structures as well as shallow structures. In our depth scaling strategy, a large damping factor is used in the early stage and then decreases automatically with the trend of error as the iteration goes on. With the depth scaling strategy, we can gradually move the parameter-searching region from shallow to deep parts. This flexible damping factor plays a role in retarding the model parameter update for shallow parts and mainly inverting deeper parts in the later stage of inversion. By doing so, we can improve deep parts in inversion results. The depth scaling strategy is applied to synthetic data without lowfrequency components for a modified version of the SEG/EAGE overthrust model. Numerical examples show that the flexible damping factor yields better results than the constant damping factor when reliable low-frequency components are missing.

• Journal of Broadcast Engineering
• /
• v.17 no.2
• /
• pp.388-399
• /
• 2012

In the paper, we propose enhanced feature extraction and matching methods for a mobile environment based on modified SURF. We propose three methods to reduce the computational complexity in a mobile environment. The first is to reduce the dimensions of the SURF descriptor. We compare the performance of existing 64-dimensional SURF with several other dimensional SURFs. The second is to improve the performance using the sign of the trace of the Hessian matrix. In other words, feature points are considered as matched if they have the same sign for the trace of the Hessian matrix, otherwise considered not matched. The last one is to find the best distance-ratio which is used to determine the matching points. We find the best distance-ratio through experiments, and it gives the relatively high accuracy. Finally, existing system which is based on normal SURF method is compared with our proposed system which is based on these three proposed methods. We present that our proposed system shows reduced response time while preserving reasonably good matching accuracy.

• Geophysics and Geophysical Exploration
• /
• v.6 no.2
• /
• pp.95-100
• /
• 2003

In this study, we developed reflection tomography inversion algorithm using Straight Ray Technique (SRT) which can calculate travel time easily and fast for complex geological structure. The inversion process begins by setting the initial velocity model as a constant velocity model that hat only impedance boundaries. The inversion process searches a layer-interface structure model that is able to explain the given data satisfactorily by inverting to minimize data misfit. For getting optimal solution, we used Gauss-Newton method that needed constructing the approximate Hessian matrix. We also applied the Marquart-Levenberg regularization method to this inversion process to prevent solution diverging. The ability of the method to resolve typical target structures was tested in a synthetic salt dome inversion. Using the inverted velocity model, we obtained the migration image close to that of the true velocity model.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.325-331
• /
• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Journal of Korea Water Resources Association
• /
• v.46 no.4
• /
• pp.389-400
• /
• 2013

In this study, a conventional pipeline unsteady friction model has been integrated into Levenberg Marquardt method to calibrate friction coefficient in a pipeline system. The method of characteristics has been employed as the modeling platform for the frequency dependant model of unsteady friction. In order to obtain Hessian and Jacobian matrix for optimization, the direct differentiation of pressure to friction factor was calculated and sensitivities to friction for heads and discharges were formulated for implementation to the integration constant in the characteristic method. Using a hypothetical simple pipeline system, time series of pressure, introduced by a sudden valve closure, were obtained for various Reynolds numbers. Convergency in fiction factors were evaluated both in steady and unsteady friction models. The comparison of calibration performance between the proposed method and genetic algorithm indicates that faster and stabler behaviour of Levenberg Marquardt method than those of evolutionary calibration.

• Proceedings of the KOSOMBE Conference
• /
• v.1991 no.05
• /
• pp.5-7
• /
• 1991

We have developed an efficient and robust image reconstruction algorithm for static impedance imaging. This improved Newton-Raphson method produced more accurate images by reducing the undesirable effects of the ill-conditioned Hessian matrix. We found that our electrical impedance tomography (EIT) system could produce two-dimensional static images from a physical phantom with 7% spatial resolution at the center and 5% at the periphery. Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations on reducing the computation time by algorithmic approaches, we implemented the improved Newton-Raphson algorithm on a parallel computer system and showed that the parallel computation could reduce the computation time from hours to minutes.