P-Least Squares Method of Curve Fitting

2013 ◽  
Vol 699 ◽  
pp. 885-892
Author(s):  
Le Min Gu
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Large Scale ◽  
Chemical Engineering ◽  
Materials Science ◽  
Least Squares Method ◽  
Chebyshev Approximation ◽  
Maximum Error ◽  
Wide Field ◽  
Curve Fitting Method

P-Least Squares (P-LS) method is Least Squares (LS) method promotion, based on the criteria of error -squares minimal to select parameter , namely satisfies following constitute the curve-fitting method. Due to the arbitrariness of the number , P-LS method has a wide field of application, when , P-LS approximation translated Chebyshev optimal approximation. This paper discusses the general principles of P-LS method; provides a way to realize the general solution of P-LS approximation. P-Least Squares method not only has significantly reduces the maximum error, also has solved the problems of Chebyshev approximation non-solution in some complex non-linear approximations，and also has the computation conveniently, can carry on the large-scale multi-data processing ability. This method is introduced by some examples unified in the materials science, the chemical engineering and the life body change.

Application of the Least Squares Support Vector Machine for Life Prediction of Vital Parts

2014 ◽  
Vol 584-586 ◽  
pp. 2129-2132
Author(s):  
Hong Kai Wang ◽  
Ji Sheng Ma ◽  
Li Qing Fang ◽  
Da Lin Wu ◽  
Yan Feng Yang
Keyword(s):  
Support Vector Machine ◽  
Least Squares ◽  
Curve Fitting ◽  
Life Prediction ◽  
Large Scale ◽  
Development Trend ◽  
Small Sample ◽  
Support Vector ◽  
Fitting Method ◽  
Curve Fitting Method

In order to better study the wear state of vital parts of the large scale equipment, and overcoming the disadvantage of small sample of vital parts, we use the least squares support vector machine (LS_SVM) algorithm to predict the wear state of vital parts. Using of quantum particle swarm optimization (QPSO) to optimize parameters least squares support vector machine, and achieved good results. Compared those with the method that use of curve fitting to predict the data development trend, show that this method is superior to the curve fitting method, and has good application value.

Curve-Fitting by the Method of Grouping

1952 ◽  
Vol 5 (2) ◽  
pp. 238
Author(s):  
PG Guest
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Least Squares Method ◽  
Normal Equations

A method of fitting polynomials is described in which the "normal" equations are obtained much more rapidly than the corresponding equations in the least-squares method. Efficiencies are found to be about 90 per cent. The method is illustrated by an example.

Research of Oilfield Production Forecast Based on Least Squares Fitting and Improved BP Neural Network

2013 ◽  
Vol 333-335 ◽  
pp. 1456-1460 ◽  
Author(s):  
Wen Bo Na ◽  
Zhi Wei Su ◽  
Ping Zhang
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Curve Fitting ◽  
Bp Neural Network ◽  
Least Squares Method ◽  
Forecast Error ◽  
Production Forecast ◽  
Least Squares Fitting ◽  
Weak Points ◽  
Lm Algorithm

A new method which is least squares fitting combined with improved BP neural network based on LM algorithm was put forward. In order to overcome the weak points that easy to fall into local minimum, slow convergence of traditional BP neural network, we use LM algorithm to improve it. Least-squares curve fitting can be used to reflect the overall trend of the data changes, so we adopted least squares method firstly to make curve fitting for sample data firstly. Then, we corrected the fitting error by the improved BP Neural Network which has the advantages that reflecting external factors. Finally, the fitted values and error correction values were added to get oilfield production forecast. The results show that the oilfield production forecast error is significantly lower than the single curve fitting, BP Neural Network or LMBP.

Detecting and Quantifying T Wave Alternans Using Linear Least Squares Curve Fitting Method

2012 ◽  
Vol 239-240 ◽  
pp. 1404-1408
Author(s):  
Xiang Kui Wan ◽  
Kang Hui Yan ◽  
Ming Gui Li
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Average ◽  
Correlation Coefficients ◽  
Linear Least Squares ◽  
T Wave ◽  
Patients At Risk ◽  
Invasive Method ◽  
T Wave Alternans ◽  
Curve Fitting Method

Evaluatement of T-wave alternans (TWA) is a non-invasive method to identify patients at risk for sudden cardiac death. A novel time-domain algorithm based on linear least squares method (LSM) for TWA analysis is developed in this paper. And the LSM’s ability to TWA analaysis in comparison with the modified moving average (MMA) method was demonstrated. In a simulation study LSM and MMA can both detected TWA with high accuracy, but under lower SNR levels LSM was found more robust, and its evaluated TWA values are closer to true TWA value. The algorithm was subsequently used to analyze the clinical ECGs from T-Wave Alternans Challenge Database, which showed that the results from this method vs. MMA had the correlation coefficients of 0.89.

Constrained Least-Squares Method for Computing Equivalent Static Wind Loads of Large-Span Roofs

2014 ◽  
Vol 17 (10) ◽  
pp. 1497-1515 ◽  
Author(s):  
Xuanyi Zhou ◽  
Ming Gu ◽  
Gang Li
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Least Squares Method ◽  
Weighting Factor ◽  
Wind Loads ◽  
Specific Response ◽  
Computational Accuracy ◽  
Constrained Least Squares ◽  
Large Span ◽  
Equivalent Static Wind Loads

Equivalent static wind loads (ESWL) are widely used by structural designers to determine a specific response of large-scale structures. However, structural designers usually pay attention to more responses. Thus, this study proposes a constrained least-squares method to compute the ESWL distribution that can simultaneously target multi-responses. The loading distribution is regarded as a linear combination of basic load distributions. Two forms of basic load distribution are presented herein. The magnitude range of ESWLs is limited by controlling the bounds of the participation factor, which can be regarded as a constrained linear least-squares problem. Furthermore, since only a few structural responses are usually emphasized by structural designers, weighting factor is imported to improve the accuracy of these focused responses. To verify its computational accuracy, the method is applied to a real large-span roof structure. The results of calculations show that a reasonable magnitude of ESWL distribution can be achieved. There seems to always be a balance between the number of targeted responses and computational accuracy.

THE USE OF A LEAST SQUARES METHOD FOR THE INTERPRETATION OF DATA FROM SEISMIC SURVEYS

Geophysics ◽  
1957 ◽  
Vol 22 (1) ◽  
pp. 9-21 ◽  
Author(s):  
A. E. Scheidegger ◽  
P. L. Willmore
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Least Squares Method ◽  
Small Scale ◽  
Simple Pattern ◽  
Seismic Surveys ◽  
Normal Equations ◽  
The Matrix

During large‐scale seismic surveys it is often impossible to arrange shot points and seismometers in a simple pattern, so that the data cannot be treated as simply as those of small‐scale prospecting arrays. It is shown that the problem of reducing seismic observations from m shot points and n seismometers (where there is no simple pattern of arranging these) is equivalent to solving (m+n) normal equations with (m+n) unknowns. These normal equations are linear, the matrix of their coefficients is symmetric. The problem of inverting that matrix is solved here by the calculus of “Cracovians,” mathematical entities similar to matrices. When all the shots have been observed at all the seismometers, the solution can even be given generally. Otherwise, a certain amount of computation is necessary. An example is given.

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