• Honam Mathematical Journal
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• v.35 no.3
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• pp.417-433
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• 2013

We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.101-124
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• 2002

The convergence rate of a numerical procedure barred on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVP's) depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It hee been observed that the Robin condition(mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. Since the convergence rate is very sensitive to the parameter, Tang[17] suggested another interface condition called over-determined interface condition. Based on the over-determined interface condition, we formulate the two-layer multi-parameterized SAM. For the SAM and the one-dimensional elliptic model BVP's, we determine analytically the optimal values of the parameters. For the two-dimensional elliptic BVP's , we also formulate the two-layer multi-parameterized SAM and suggest a choice of multi-parameter to produce good convergence rate .

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.477-488
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• 2012

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the mixed interface condition, controlled by a parameter, can optimize SAM's convergence rate. In [8], one introduced the two-layer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. In this paper, we present a method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.161-171
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• 2011

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [7], one had formulated the multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. However it was not successful for two-dimensional problem. In this paper, we present a new method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.

• Journal of information and communication convergence engineering
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• v.2 no.1
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• pp.36-39
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• 2004

In this paper, a method of improving the learning speed and convergence rate is proposed to exploit the advantages of artificial neural networks and neuro-fuzzy systems. This method is applied to the XOR problem, n bit parity problem, which is used as the benchmark in the field of pattern recognition. The method is also applied to the recognition of digital image for practical image application. As a result of experiment, it does not always guarantee convergence. However, the network showed considerable improvement in learning time and has a high convergence rate. The proposed network can be extended to any number of layers. When we consider only the case of the single layer, the networks had the capability of high speed during the learning process and rapid processing on huge images.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.507-516
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• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.329-341
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• 2004

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.

• Journal of Korea Multimedia Society
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• v.24 no.11
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• pp.1481-1491
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• 2021

Since most biosignals rely on contact-based measurement, there is still a problem in that it is hard to provide convenience to users by applying them to daily life. In this paper, we present a mobile application for estimating heart rate based on a deep learning model. The proposed application measures heart rate by capturing real-time face images in a non-contact manner. We trained a three-dimensional convolutional neural network to predict photoplethysmography (PPG) from face images. The face images used for training were taken in various movements and situations. To evaluate the performance of the proposed system, we used a pulse oximeter to measure a ground truth PPG. As a result, the deviation of the calculated root means square error between the heart rate from remote PPG measured by the proposed system and the heart rate from the ground truth was about 1.14, showing no significant difference. Our findings suggest that heart rate measurement by mobile applications is accurate enough to help manage health during daily life.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.177-181
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• 2004

In this paper, we suggest an Iris recognition system with an excellent recognition rate and confidence as an alternative biometric recognition technique that solves the limit in an existing individual discrimination. For its implementation, we extracted coefficients feature values with the wavelet transformation mainly used in the signal processing, and we used neural network to see a recognition rate. However, Scale Conjugate Gradient of nonlinear optimum method mainly used in neural network is not suitable to solve the optimum problem for its slow velocity of convergence. So we intended to enhance the recognition rate by using Levenberg-Marquardt Back-propagation which supplements existing Scale Conjugate Gradient for an implementation of the iris recognition system. We improved convergence velocity, efficiency, and stability by changing properly the size according to both convergence rate of solution and variation rate of variable vector with the implementation of an applied algorithm.