• Journal of the Korean Society of Propulsion Engineers
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• v.3 no.2
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• pp.1-9
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• 1999

Applicability of the pressure gradient method which is formulated based on pressure gradient is verified against turbulent flow analysis. In the pressure gradient method, pressure gradient instead of pressure itself is obtained using continuity constraint. Since correct pressure gradient is found only when mass conservation is satisfied, pressure gradient method can reflect physics of flow field properly The pressure gradient method is formulated with semi-staggered grid system which locates each primitive variables on the same grid point but evaluates pressure gradient in-between. This grid system ensures easy programming and reflection of correct physics in analysis. For verifying applicability of this method, the pressure gradient method is applied to turbulent flow analysis with low Reynolds number $\kappa$-$\varepsilon$ model. Turbulent flows include fully developed channel flow, backward-facing step flow, and conical diffuser flow. Prediction results show that the pressure gradient method can be applied to turbulent flow analysis. However, the pressure gradient method requires somewhat long computation time. Proper way to find optimum under-relaxation factor, $\gamma$, is also need to be developed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.91-104
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• 2004

A modification of the gradient method of convex programming is introduced. Also, we describe symbolic implementation of the gradient method and its modification by means of the programming language MATHEMATICA. A few numerical examples are reported.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1595-1597
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• 1987

Two gradient methods, steepest descent method and conjugate gradient descent method, are compar ed through application to vector linear predictors. It is found that the convergence rate of the conju-gate gradient descent method is much faster than that of the steepest descent method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• Journal of Practical Engineering Education
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• v.14 no.2
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• pp.305-312
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• 2022

In this paper, we focused on training to create and optimize a basic data prediction model. And we proposed a gradient descent training method of machine learning that is widely used to optimize data prediction models. It visually shows the entire operation process of gradient descent used in the process of optimizing parameter values required for data prediction models by applying the differential method and teaches the effective use of mathematical differentiation in machine learning. In order to visually explain the entire operation process of gradient descent, we implement gradient descent SW in a spreadsheet. In this paper, first, a two-variable gradient descent training method is presented, and the accuracy of the two-variable data prediction model is verified by comparison with the error least squares method. Second, a three-variable gradient descent training method is presented and the accuracy of a three-variable data prediction model is verified. Afterwards, the direction of the optimization practice for gradient descent was presented, and the educational effect of the proposed gradient descent method was analyzed through the results of satisfaction with education for non-majors.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.444-449
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• 2006

Path planning is a key element in navigation of a mobile robot. Several algorithms such as a gradient method have been successfully implemented so for. Although the gradient method can provide the global optimal path, it computes the navigation function over the whole environment at all times, which result in high computational cost. This paper proposes a high-speed path planning scheme, called a gradient method with topological information, in which the search space for computation of a navigation function can be remarkably reduced by exploiting the characteristics of the topological information reflecting the topology of the navigation path. The computing time of the gradient method with topological information can therefore be significantly decreased without losing the global optimality. This reduced path update period allows the mobile robot to find a collision-free path even in the dynamic environment.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.197-205
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• 2007

We have proposed a novel line detection method based on the estimated probability density function of gradient directions of edges. By estimating peaks of the density function, we determine groups of edges that have the same gradient direction. For edges in the same groups, we detect lines that correspond to peaks of the connectivity weighted distribution of the distances from the origin. In the experiments using the Data Matrix barcode images and LCD images, the proposed method showed better performance than conventional Methods in terms of the processing speed and accuracy.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Journal of Fisheries and Marine Sciences Education
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• v.20 no.2
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• pp.156-167
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• 2008

Meorological data have been collected to monitor the wetland area in Goheung bay since 2003 and four intensive observations were conducted to study effects of the atmospheric turbulence on the energy budget and the ecological changes. We improved an algorithm to estimate the sensible heat flux with routine data. The sensible heat flux estimated by gradient method was in good agreement with that measured by precision instruments such as surface layer scintillometer and ultrasonic anemometer. Diurnal variations of sensible heat flux showed analogous tendency to those of temperature gradient. When the vertical wind shear of horizontal wind components was weak, even though temperature gradient was strong, the gradient method underestimated the sensible heat flux. A compensation for the cloud will make this gradient method be a helpful tool to monitor the ecosystem without expensive instruments except for weak wind shear and temperature gradient.