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DUAL REGULARIZED TOTAL LEAST SQUARES SOLUTION FROM TWO-PARAMETER TRUST-REGION ALGORITHM
Lee, Geunseop Korean Mathematical Society 2017 대한수학회지 Vol.54 No.2
For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.
Room-temperature growth of Mg on Si(111): stepwise versus continuous deposition
Lee, Dohyun,Lee, Geunseop,Kim, Sehun,Hwang, Chanyong,Koo, Ja-Yong,Lee, Hangil IOP Pub 2007 Journal of physics, an Institute of Physics journa Vol.19 No.26
<P>Using low-energy electron diffraction and scanning tunnelling microscopy, we studied the formation of Mg silicide and metallic Mg islands on a Si(111)-7 ? 7 surface at room temperature as a function of Mg coverage. We found that the mechanism by which Mg islands grew on the Si(111)-7 ? 7 surface, and the morphology of the islands that formed, depended on whether the Mg deposition was performed in a stepwise or continuous manner. When Mg was deposited in a stepwise manner, with 1?h between deposition events, an amorphous Mg silicide overlayer formed on the Si(111)-7 ? 7 surface during the initial stage of deposition (up to 2.0?ML Mg coverage), as shown by the observation of δ7 ? 7 and 1 ? 1 low-energy electron diffraction patterns. Upon further stepwise Mg deposition, round-shaped Mg islands grew on the amorphous Mg silicide layer, as shown by scanning tunnelling microscopy and the emergence of a 1 ? 1 low-energy electron diffraction pattern. If, on the other hand, the Mg was deposited continuously in a single step, hexagonal Mg islands formed on the flat Mg silicide layers, and a <img SRC='http://ej.iop.org/images/0953-8984/19/26/266004/cm243037ieqn1.gif' ALIGN='MIDDLE' ALT='({{2 \over 3} \sqrt {3}} \times {{2 \over 3} \sqrt {3}})\mathrm {R}30 ^{\circ } '/> and 1 ? 1 mixed phase was observed. Moreover, using scanning tunnelling spectroscopy, we confirmed the semiconducting and metallic nature of the Mg silicide layer and hexagonal Mg islands on the Si(111)-7 ? 7 surface depending on their Mg coverage, respectively. </P>
Interaction and surface photovoltage effect of MoS2 with Na deposition
Lee Wonhui,Lee Sangsoo,Lee Geunseop 한국물리학회 2024 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.84 No.5
Using photoelectron spectroscopy (PES) with synchrotron radiation (SR), we investigated the interaction of a MoS2 surface with Na. When Na was deposited at room temperature and at low temperature (~ 90 K), the PES data showed that both the core levels and the valence band shifted toward high binding by almost the same energies, compared with the pristine surface. This indicates that the deposited Na interacted non-reactively with MoS2, while inducing a rigid shift of the PES peaks by donating electrons to the MoS2 substrate. Deposition of sufcient amount of Na allowed the conduction band of MoS2 to be partially flled, revealing a clear Fermi edge. For Na deposition at low temperature, the Fermi edge appeared above the reference Fermi level. We attribute this to the surface photovoltage (SPV) efect generated by SR light. The SPV was measured to decrease when the sample was heated, refecting the increasing recombination of SR-generating electron–hole pairs with increasing temperature.
Lee, Geunseop Korean Mathematical Society 2017 대한수학회지 Vol.54 No.5
The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.
AN EFFICIENT ALGORITHM FOR SLIDING WINDOW BASED INCREMENTAL PRINCIPAL COMPONENTS ANALYSIS
Lee, Geunseop Korean Mathematical Society 2020 대한수학회지 Vol.57 No.2
It is computationally expensive to compute principal components from scratch at every update or downdate when new data arrive and existing data are truncated from the data matrix frequently. To overcome this limitations, incremental principal component analysis is considered. Specifically, we present a sliding window based efficient incremental principal component computation from a covariance matrix which comprises of two procedures; simultaneous update and downdate of principal components, followed by the rank-one matrix update. Additionally we track the accurate decomposition error and the adaptive numerical rank. Experiments show that the proposed algorithm enables a faster execution speed and no-meaningful decomposition error differences compared to typical incremental principal component analysis algorithms, thereby maintaining a good approximation for the principal components.