• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.643-652
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• 2002

This paper proposes an efficient hybrid fixed-point (FP) algorithm for improving performances of the independent component analysis (ICA) based on neural networks. The proposed algorithm is the FP algorithm based on secant method and momentum for ICA. Secant method is applied to improve the separation performance by simplifying the computation process for estimating the root of objective function, which is to minimize the mutual informations of the independent components. The momentum is applied for high-speed convergence by restraining the oscillation if the process of converging to the optimal solution. It can simultaneously achieve a superior properties of the secant method and the momentum. The proposed algorithm has been applied to the composite fingerprints and the images generated by random mixing matrix in the 8 fingerprints of $256\times{256}$-pixel and the 10 images of $512\times{512}$-pixel, respectively. The simulation results show that the proposed algorithm has better performances of the separation speed and rate than those using the FP algorithm based on Newton and secant method. Especially, the secant FP algorithm can be solved the separating performances depending on initial points settings and the nonrealistic learning time for separating the large size images by using the Newton FP algorithm.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.05a
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• pp.498-501
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• 2004

A new slab design using secant stiffness, Direct Inelastic Slab Design, was developed. Since basically the proposed design method uses linear analysis, it is convenient and stable in numerical analysis. At the same time, the proposed design method can accurately estimate the inelastic strength and ductility demands of slab because it can analyzes the inelastic behavior of structure using iterative calculations for secant stiffness. In the present study, the procedure of the proposed design method was established, and a computer program incorporating the proposed method was developed. Design examples using the proposed method were presented, and compared with traditional nonlinear analysis, and experiments. The Direct Inelastic Slab Design, as an integrated analysis/design method, can directly address the design strategy intended by the engineer, such as moment strength and ductility limit. As a result, economical and safe design can be achieved.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.336-341
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• 2004

This paper proposes an independent component analysis(ICA) of the fixed-point (FP) algorithm based on secant method and the kurtosis. The FP algorithm based on secant method is applied to improve the analysis speed and performance by simplifying the calculation process of the complex derivative in Newton method, the kurtosis is applied to cluster the components. The proposed ICA has been applied to the problems for separating the 6-mixed signals of 500 samples and 8-mixed images of $512{\times}512$ pixels, respectively. The experimental results show that the proposed ICA has always a fixed analysis sequence. The result can be solved the limit of conventional ICA based on secant method which has a variable sequence depending on the running of algorithm. Especially, the proposed ICA can be used for classifying and identifying the signals or the images.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.17-28
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• 2018

In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.845-852
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• 2010

A nonlinear algebraic equation f(x) = 0 is considered to find a root with integer multiplicity $m{\geq}1$. A variant of Newton-secant method for a multiple root is proposed below: for n = 0, 1, $2{\cdots}$ $$x_{n+1}=x_n-\frac{f(x_n)^2}{f^{\prime}(x_n)\{f(x_n)-{\lambda}f(x_n-\frac{f(x_n)}{f^{\prime}(x_n)})\}$$, $$\lambda=\{_{1,\;if\;m=1.}^{(\frac{m}{m-1})^{m-1},\;if\;m{\geq}2$$ It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numerical examples successfully verified the proposed scheme with high-precision Mathematica programming.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.985-988
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• 2008

A linear analysis method using reduced secant stiffness was developed for inelastic earthquake design of reinforced concrete structures. In the proposed method, the beam-column element and plane element, which are the same as used in conventional elastic analysis, are used for structural modeling. Based on the structural plastic mechanism intended by engineer, the distribution of inelastic members is determined. The secant stiffness of the inelastic members is determined based on the target ductility of the structure. Inelastic strengths of the members are calculated by using linear analysis on the structure modeled with secant stiffness. Plastic rotations in the inelastic members are calculated with the nodal rotations resulting from the secant stiffness analysis. For verification, the proposed method was applied to the inelastic earthquake designs of a moment-resisting frame and a dual system of two dimensions, and also a dual system of three dimensions.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.294-299
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• 2005

This paper presents the separation performance of the linearly mixed image signals with additive noises by using an independent component analyses(ICAs) of the fixed-point(FP) algorithm based on Newton and secant method, respectively. The Newton's FP-ICA uses the slope of objective function, and the secant's FP-ICA also uses the tangent line of objective function. The 2 kinds of ICA have been applied to the 2 dimensional 2-image with $512\times512$ pixels. Then Gaussian noise and Laplacian noise are added to the mixed images, respectively. The experimental results show that the Newton's FP-ICA has better the separation speed than secant FP-ICA and the secant's FP-ICA has also the better separation rate than Newton's FP-ICA. Especially, the Newton and secant method gives relatively larger improvement degree in separation speed and rate as the noise increases.

• East Asian mathematical journal
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• v.24 no.1
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• pp.21-25
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• 2008

The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.03a
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• pp.85-92
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• 2003

Hysteretic behaviors of a seismic isolator are identified by using the regularized output error estimator (OEE) based on the secant stiffness model. A proper regularity condition of tangent stiffness for the current OEE is proposed considering the regularity condition of Duhem hysteretic operator. The proposed regularity condition is defined by 12-norm of the tangent stiffness with respect to time. The secant stiffness model for the OEE is obtained by approximating the tangent stiffness under the proposed regularity condition by the secant stiffness at each time step. A least square method is employed to minimize the difference between the calculated response and measured response for the OEE. The regularity condition of the secant stiffness is utilized to alleviate ill-posedness of the OEE and to yield numerically stable solutions through the regularization technique. An optimal regularization factor determined by geometric mean scheme (GMS) is used to yield appropriate regularization effects on the OEE.

• The KIPS Transactions:PartB
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• v.11B no.7 s.96
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• pp.813-820
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• 2004

This paper proposes a digital image watermarking which is robust to geometric distortions using an independent component analysis(ICA) of fixed-point(FP) algorithm based on secant method. The FP algorithm of secant method is applied for better performance in a separation time and rate, and ICA is applied to reject the prior knowledges for original image, key, and watermark such as locations and size, etc. The proposed method embeds the watermark into the spatial domain of original image The proposed watermarking technique has been applied to lena, key, and two watermarks(text and Gaussian noise) respectively. The simulation results show that the proposed method has higher speed and better rate for extracting the original images than the FP algorithm of Newton method. And the proposed method has a watermarking which is robust to geometric distortions such as resizing, rotation, and cropping. Especially, the watermark of images with Gaussian noise has better extraction performance than the watermark with text since Gaussian noise has lower correlation coefficient than the text to the original and key images. The watermarking of ICA doesn't require the prior knowledge for the original images.