scholarly journals Improvement of the Approximation Accuracy of LED Radiation Patterns

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 337 ◽  
Author(s):  
Ivan Rachev ◽  
Todor Djamiykov ◽  
Marin Marinov ◽  
Nikolay Hinov
Keyword(s):  
Least Squares ◽  
Mathematical Analysis ◽  
Least Squares Method ◽  
Weighting Function ◽  
Radiation Patterns ◽  
Approximation Accuracy ◽  
Light Emitting ◽  
Approximation Function ◽  
Wide Range ◽  
Optoelectronic Systems

For the great variety of light-emitting diodes (LEDs), there exists a wide range of LED radiation patterns. An approach for constructing patterns of higher accuracy is here considered. The latter is required when the design of optoelectronic systems or their optimization is carried out analytically. A weighting function is introduced that allows increasing the gradient of the diagram of different widths. It has been selected through mathematical analysis of the emission diagrams of different LEDs used in optoelectronic systems. Based on the least squares method an algorithm is created, and programs are developed in MATLAB environment to estimate the parameters of the approximation function. Its accuracy is evaluated by comparison with the approximation with Lambert source of order n. The results show higher accuracy of the proposed approximation function compared to those obtained by conventional methods. Recommendations on the application of the proposed approach are given.

Integration of Moving Least Squares Method and Multilevel B-Spline Method for Scattered Data Approximation

2011 ◽  
Vol 291-294 ◽  
pp. 2245-2249
Author(s):  
Shi Ju Yan ◽  
Bin Ge
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Scattered Data ◽  
Moving Least Squares ◽  
Scattered Data Approximation ◽  
Approximation Accuracy ◽  
Data Approximation ◽  
B Spline ◽  
Moving Least Squares Method ◽  
Method Accuracy

For scattered data approximation with multilevel B-spline(MBS) method, accuracy could be enhanced by densifying control lattice. Nevertheless, when control lattice density reaches to some extent, approximation accuracy could not be enhanced further. A strategy based on integration of moving least squares(MLS) and multilevel B-spline(MBS) is presented. Experimental results demonstrate that the presented strategy has higher approximation accuracy.

A Simplified Interpolating Moving Least-Squares Method and its Error Estimates

2011 ◽  
Vol 101-102 ◽  
pp. 271-274
Author(s):  
Ju Feng Wang
Keyword(s):  
Error Estimate ◽  
Least Squares ◽  
Shape Function ◽  
Least Squares Method ◽  
Delta Function ◽  
Moving Least Squares ◽  
Approximation Function ◽  
Kronecker Delta ◽  
Moving Least Squares Method ◽  
Mls Approximation

A disadvantage of the MLS approximation is that the shape function of this method does not satisfy the property of Kronecker Delta function. Thus developing an interpolating MLS approximation is very important. In this paper, the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas is discussed in detail and a simplified expression of the approximation function of the IMLS method is given. The simpler expression makes it more convenient to use this method. The error estimate of the approximation function also is discussed. And a numerical example is given to confirm the results.

scholarly journals IN INTERPOLATING THE VALUES OF FUNCTIONS SPECIFIED BY THE TABLE EFFECTIVENESS OF THE LEAST SQUARES METHOD

2020 ◽  
pp. 68-71
Author(s):  
М.Е. Eskaliyev ◽  
◽  
А.А. Masimgazieva ◽  
N.A. Nurgali ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Main Idea ◽  
Gram Matrix ◽  
Method Of Least Squares ◽  
Newton Interpolation ◽  
Wide Range ◽  
Mathematical Formulas ◽  
The Difference ◽  
Interpolation Polynomials

The article provides a general algorithm of the method of least squares (OLS) for the compilation of a program account, taking into account the features of the Gram matrix. In fact, the difference and advantage of the OLS from the long-known Langrange and Newton interpolation polynomials is emphasized. Using the general MNC algorithm, the square version of the MNC is considered. The characteristic of the full algorithm of the square version is given using special selected mathematical formulas. The scope of OLS in household and practical computational problems is indicated. The application of the least squares method has a wide range, especially for geographical forecasts, hydrometeorological control, and dosage of geological resources. Therefore, for applied calculations, DVI is used for more accurate calculation of approximate values of functions that are suitable in some values and are presented in the form of tables. Its main idea is to create a function and correct deviations caused by errors made during measurement.

scholarly journals Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhisong Xu ◽  
Mingqiu Li
Keyword(s):  
Fractional Calculus ◽  
Quadratic Programming ◽  
Frequency Domain ◽  
Frequency Band ◽  
Rational Approximation ◽  
Least Squares Method ◽  
Approximation Accuracy ◽  
Approximation Function ◽  
Fractional Calculus Operators ◽  
Quadratic Programming Method

When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the error criterion of the least squares method, a quadratic programming method based on the frequency-domain error is proposed. In this method, the frequency-domain error minimization between the fractional operator s ± r and its rational approximation function is transformed into a quadratic programming problem. The results show that the construction method of the optimal rational approximation function of fractional calculus operator is effective, and the optimal rational approximation function constructed can effectively approximate the fractional calculus operator and model for the specified approximation frequency band.

scholarly journals On the Use of Weighted Least Squares for Time Domain Modal Parameter Identification

2004 ◽  
Vol 11 (3-4) ◽  
pp. 457-465 ◽  
Author(s):  
Jonathan E. Cooper
Keyword(s):  
Parameter Identification ◽  
Least Squares ◽  
Time Domain ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Computational Effort ◽  
High Signal ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Wide Range

An approach for the use of the Weighted Least Squares method for time domain modal parameter identification is introduced. The approach enables standard identification methods to be employed in the usual manner, except that sections of the time records with high signal-noise ratios are given a greater emphasis in the identification process. It is shown how it is possible to apply the method to a wide range of applications, including the analysis of impulse response, input-output and time varying data. A number of different weighting schemes are explored, based upon exponential weighting and the envelope of the measured data. A series of simulated tests demonstrate how the performance of conventional time domain algorithms can be improved significantly with little extra computational effort though the use of a Weighted Least Squares scheme.

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

2011 ◽  
Vol 18 (3) ◽  
pp. 379-390 ◽  
Author(s):  
Józef Borkowski
Keyword(s):  
Least Squares ◽  
Linear Approximation ◽  
Least Squares Method ◽  
Analytical Form ◽  
Linear Functions ◽  
Approximation Solution ◽  
Approximation Accuracy ◽  
Approximation Characteristic ◽  
Zero Padding ◽  
Approximation Parameter

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

scholarly journals A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2424
Author(s):  
Jufeng Wang ◽  
Fengxin Sun ◽  
Rongjun Cheng
Keyword(s):  
Least Squares ◽  
Splitting Method ◽  
Weak Form ◽  
Moving Least Squares ◽  
Weight Functions ◽  
High Approximation ◽  
Approximation Accuracy ◽  
Approximation Function ◽  
Discrete Equations ◽  
The Matrix

By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy.

Study on Forecasting of Gold Price Based on Varying-Coefficient Regression Model

2011 ◽  
Vol 467-469 ◽  
pp. 1398-1403
Author(s):  
Qi Zhang ◽  
Jun Hai Ma ◽  
Yan Wang
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Cross Validation ◽  
Least Squares Method ◽  
Weighting Function ◽  
Weighted Least Squares ◽  
Gold Price ◽  
Varying Coefficient ◽  
Sample Data ◽  
Varying Coefficient Regression

U.S. dollar index, oil prices, silver prices, DOW index, OECD leading index and the CRB index are selected and varying-coefficient regression model which has dynamic response to the various variables influence is applied to predict the gold price and improve the prediction accuracy in this paper. In addition, the weighted least squares is adopted as an estimation of the parameters, corrects the traditional least squares method defect which assumes the sample data weights equal points to the prediction, making sample weights larger closer with prediction points. In the choice of weighting function, the paper uses cross validation to gain smoothing parameter. In the last, we predicted the 12 months gold prices from January 2010 December 2010 applies varying-coefficient regression model.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method
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