Focusing of Laser Beams through Scattering Medium by Golden Section Method

2017 ◽  
Author(s):  
Ziyang Chen ◽  
Xiansheng Hu ◽  
Xuanxuan Ji ◽  
Jixiong Pu
Keyword(s):  
Golden Section ◽  
Laser Beams ◽  
Scattering Medium ◽  
Section Method ◽  
Golden Section Method

ON THE ACCELERATION OF OPTIMIZATION METHODS FOR THE PROBLEM OF SYNTHESIS OF MULTILAYER OPTICAL COATINGS

2021 ◽  
Vol 6 ◽  
pp. 13-26
Author(s):  
Alexander Mitsa ◽  
◽  
Petr Stetsyuk ◽  
Alexander Levchuk ◽  
Vasily Petsko ◽  
...  
Keyword(s):  
Objective Function ◽  
Golden Section ◽  
Optical Coatings ◽  
Generalized Gradient ◽  
Arithmetic Operations ◽  
Section Method ◽  
Suffix Arrays ◽  
Multidimensional Search ◽  
Golden Section Method ◽  
Speed Up

Five ways to speed up the multidimensional search in order to solve the problem of synthesis of multilayer optical coatings by using the methods of zero and first orders have been considered. The first way is to use an analytical derivative for the target quality function of the multilayer coating. It allows us to calculate accurately (within the computer arithmetic) the value of the gradient of a smooth objective function and generalized gradient of a non-smooth objective one. The first way requires the same number of arithmetic operations as well as finite-difference methods of calculating the gradient and the generalized gradient. The second way is to use a speedy finding of the objective function gradient using the prefix- and suffix-arrays in the analytical method of calculating the gradient. This technique allows us to reduce the number of arithmetic operations thrice for large-scale problems. The third way is the use of tabulating the values of trigonometric functions to calculate the characteristic matrices. This technique reduces the execution time of multiplication operations of characteristic matrices ten times depending on the computer’s specifications. For some computer architectures, this advantage is more than 140 times. The fourth method is the use of the golden section method for the one-dimensional optimization in the problems of synthesis of optical coatings. In particular, when solving one partial problem it is shown that the ternary search method requires approximately 40% more time than the golden section method. The fifth way is to use the effective implementation of multiplication of two matrices. It lies in changing the order of the second and third cycles for the well-known method of multiplying two matrices and fixing in a common variable value of the element of the first matrix. This allows us to speed up significantly the multiplication operation of two matrices. For matrices having 1000 x 1000 dimension the acceleration is from 2 to 15 times, depending on the computer's specifications.

Focusing of Scattering Light by Improved Feedback Wavefront Shaping Technique Based on Golden Section Method

2017 ◽  
Vol 37 (6) ◽  
pp. 0626005
Author(s):  
胡显声 Hu Xiansheng ◽  
蒲继雄 Pu Jixiong ◽  
冀旋旋 Ji Xuanxuan ◽  
陈子阳 Chen Ziyang
Keyword(s):  
Golden Section ◽  
Section Method ◽  
Shaping Technique ◽  
Golden Section Method ◽  
Wavefront Shaping ◽  
Scattering Light

PARAMETER OPTIMIZATION OF SINGLE EXPONENTIAL SMOOTHING USING GOLDEN SECTION METHOD FOR GROCERIES FORECASTING

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Vivi Aida Fitria
Keyword(s):  
Golden Section ◽  
Exponential Smoothing ◽  
Food Prices ◽  
Percentage Error ◽  
Boundary Area ◽  
Section Method ◽  
Golden Section Method ◽  
Long Time ◽  
Exponential Smoothing Method ◽  
Single Exponential

Department of Agriculture and Food Security Malang City, especially in the Field of Food Supply Availability and Distribution requires a reference forecasting of food prices in Malang. The method used in the forecasting calculation is Single Exponential Smoothing. In the process of calculating the Single Exponential Smoothing method, it takes alpha parameters between 0 and 1. The problem is when to estimate the alpha value between 0 to 1 with trial error with the aim of producing minimal forecasting results. Therefore, this study aims to determine the optimal alpha value. The method used in this research is the Golden Section Method. The principle of Golden Section method in this study is to reduce the boundary area so as to produce a minimum MAPE (Mean Absolute Percentage Error) value The data used in this study is the price of 9 commodities of Groceries in Malang since January 1, 2016 until December 31, 2017. The results showed that the Golden Section method found that the optimal alpha value was 0.999 with MAPE average of 9 commodities is 0.79%. So with this golden section method researchers do not need a long time to determine alpha by trial error

Optimization of Thickness Uniformity for Two Times Spray Technology

2014 ◽  
Vol 633-634 ◽  
pp. 675-678 ◽  
Author(s):  
Yong Zeng ◽  
Wen Wei Zha
Keyword(s):  
Coating Thickness ◽  
Optimization Model ◽  
Optimization Problem ◽  
Golden Section ◽  
Optimization Method ◽  
Section Method ◽  
Thickness Uniformity ◽  
Coating Uniformity ◽  
Result Show ◽  
Golden Section Method

Due to the optimization problem of coating thickness uniformity for two times spray technology, an optimization method of coating thickness uniformity for two times spray technology was proposed based on the optimized spray trajectory of one time. Based on the established tool model and complex curved surface was partitioned into several plane patches, the model of coating thickness was established for two times spray on the plane. The optimization model of coating uniformity was given and the golden section method was used to solve it. Simulation result show that the feasibility and availability of optimization model; the coating uniformity was improved effectively after optimization for two times spray trajectory.

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