scholarly journals Self-similar factor approximants

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
S. Gluzman ◽  
V. I. Yukalov ◽  
D. Sornette
Keyword(s):  
2003 ◽  
Vol 328 (3-4) ◽  
pp. 409-438 ◽  
Author(s):  
V.I. Yukalov ◽  
S. Gluzman ◽  
D. Sornette

2020 ◽  
Vol 34 (21) ◽  
pp. 2050208
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters, are often of main physical interest. A method is described for predicting the large-variable behavior of solutions to nonlinear problems from the knowledge of only their small-variable expansions. The method is based on self-similar approximation theory resulting in self-similar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the self-similar predictions can be compared with the available large-variable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of small-variable expansions. Numerical convergence of approximants is demonstrated.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Dong Zhao

Due to significant differences in imaging mechanisms between multimodal images, registration methods have difficulty in achieving the ideal effect in terms of time consumption and matching precision. Therefore, this paper puts forward a rapid and robust method for multimodal image registration by exploiting local edge information. The method is based on the framework of SURF and can simultaneously achieve real time and accuracy. Due to the unpredictability of multimodal images’ textures, the local edge descriptor is built based on the edge histogram of neighborhood around keypoints. Moreover, in order to increase the robustness of the whole algorithm and maintain the SURF’s fast characteristic, saliency assessment of keypoints and the concept of self-similar factor are presented and introduced. Experimental results show that the proposed method achieves higher precision and consumes less time than other multimodality registration methods. In addition, the robustness and stability of the method are also demonstrated in the presence of image blurring, rotation, noise, and luminance variations.


2009 ◽  
Vol 107 (21) ◽  
pp. 2237-2244 ◽  
Author(s):  
V.I. Yukalov ◽  
S. Gluzman
Keyword(s):  

2008 ◽  
Vol 323 (12) ◽  
pp. 3074-3090 ◽  
Author(s):  
E.P. Yukalova ◽  
V.I. Yukalov ◽  
S. Gluzman

2007 ◽  
Vol 368 (5) ◽  
pp. 341-347 ◽  
Author(s):  
V.I. Yukalov ◽  
E.P. Yukalova
Keyword(s):  

2004 ◽  
Vol 18 (22) ◽  
pp. 3027-3046 ◽  
Author(s):  
V. I. YUKALOV ◽  
S. GLUZMAN

The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on self-similar factor and root approximants, suggested earlier by the authors. It is shown that these approximants and their combinations can effectively extrapolate power series to the region of large variables, even up to infinity. Several examples from quantum and statistical mechanics are analyzed, illustrating the approach.


2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  

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