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Your search keyword '"Lee, Tsung-Lin"' showing total 166 results
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166 results on '"Lee, Tsung-Lin"'

8. Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method

Author

Lee, Tsung-Lin and Kuo, Yueh-Cheng

Subjects
Mathematics - Numerical Analysis
Abstract

The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only depends on the dimension of the tensor and the proof is constructive. Under these conditions, an algorithm applying homotopy continuation method is developed for computing the CP decomposition of tensors.

Published
2016

10. Adaptive Linked-List Mechanism for Wi-Fi Wireless Network

Author

Lee, Tsung-Lin, Chiu, Jih-Ching, Li, Yueh-Lin, Barbosa, Simone Diniz Junqueira, Editorial Board Member, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Yuan, Junsong, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Chang, Chuan-Yu, editor, Lin, Chien-Chou, editor, and Lin, Horng-Horng, editor

Published
2019
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12. Seven mutually touching infinite cylinders

Author

Bozóki, Sándor, Lee, Tsung-Lin, and Rónyai, Lajos

Subjects
Mathematics - Metric Geometry, Computer Science - Computational Geometry, 52C17, 52A40, 65H04, 65H20, 65G40
Abstract

We solve a problem of Littlewood: there exist seven infinite circular cylinders of unit radius which mutually touch each other. In fact, we exhibit two such sets of cylinders. Our approach is algebraic and uses symbolic and numerical computational techniques. We consider a system of polynomial equations describing the position of the axes of the cylinders in the 3 dimensional space. To have the same number of equations (namely 20) as the number of variables, the angle of the first two cylinders is fixed to 90 degrees, and a small family of direction vectors is left out of consideration. Homotopy continuation method has been applied to solve the system. The number of paths is about 121 billion, it is hopeless to follow them all. However, after checking 80 million paths, two solutions are found. Their validity, i.e., the existence of exact real solutions close to the approximate solutions at hand, was verified with the alphaCertified method as well as by the interval Krawczyk method., Comment: 13 pages, 2 figures

Published
2013
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13. Central Configurations of the Five-Body Problem with Equal Masses

Author

Lee, Tsung-Lin and Santoprete, Manuele

Subjects
Mathematical Physics
Abstract

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

Published
2009
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20. Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods

Author

Chen, Tianran, Lee, Tsung-Lin, Li, Tien-Yien, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Hong, Hoon, editor, and Yap, Chee, editor

Published
2014
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32. Solvent polarity tuning to enhance the crystallinity of 2D-covalent organic frameworks for visible-light-driven hydrogen generation

Author

Elewa, Ahmed M., primary, EL-Mahdy, Ahmed F. M., additional, Hassan, Ahmed E., additional, Wen, Zhenhai, additional, Jayakumar, Jayachandran, additional, Lee, Tsung-Lin, additional, Ting, Li-Yu, additional, Mekhemer, Islam M. A., additional, Huang, Tse-Fu, additional, Elsayed, Mohamed Hammad, additional, Chang, Chih-Li, additional, Lin, Wei-Cheng, additional, and Chou, Ho-Hsiu, additional

Published
2022
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44. A new family of generalized quadrature methods for solving nonlinear equations.

Author

Liu, Chein-Shan and Lee, Tsung-Lin

Subjects
NONLINEAR equations, ARITHMETIC mean, NEWTON-Raphson method
Abstract

Weerakoon and Fernando [A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000) 87–93] were resorted on a trapezoidal quadrature rule to derive an arithmetic mean Newton method with third-order convergence of the iterative scheme to solve nonlinear equations. Different quadrature methods have been developed, which form a special class of third-order iterative schemes requiring three evaluations of functions on [ f (x n) , f ′ (x n) , f ′ (y n) ] per iteration, where y n is generated from the first Newton step. As an extension of these methods, we derive a new family of iterative schemes by using a new weight function H to generalize the quadrature methods, of which (x n + 1 − x n) f ′ (x n) / H signifies an approximate area under the curve f ′ (x) between x n and x n + 1 . Then, a generalization of the midpoint Newton method is obtained by using another weight function, which is based on three evaluations of functions on [ f (x n) , f ′ (x n) , f ′ ((x n + y n) / 2) ] per iteration. The sufficient conditions of these two weight functions are derived, which guarantee that the convergence order of the proposed iterative schemes is three. [ABSTRACT FROM AUTHOR]

Published
2022
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