ABS Algorithms for Linear Equations and Linear Least Squares

2012 ◽  
Keyword(s):  
Least Squares ◽  
Linear Equations ◽  
Linear Least Squares ◽  
Abs Algorithms

ABS Algorithms for Linear Equations and Linear Least Squares

2006 ◽  
pp. 12-18
Author(s):  
Emilio Spedicato
Keyword(s):  
Least Squares ◽  
Linear Equations ◽  
Linear Least Squares ◽  
Abs Algorithms

Boundary Extension Technique for HHT Based on Response Surface Method

2012 ◽  
Vol 256-259 ◽  
pp. 2854-2862
Author(s):  
Ling Bai ◽  
Jin Zhao Liu ◽  
Ai Min Xu ◽  
Xing Fang
Keyword(s):  
Least Squares ◽  
Response Surface ◽  
Response Surface Method ◽  
Linear Equations ◽  
Hessian Matrix ◽  
Extension Problem ◽  
Boundary Extension ◽  
Linear Least Squares ◽  
Least Squares Problem ◽  
Surface Method

HHT is widely used to analyze nonlinear and non-stationary signals. But how to extend boundaries of signals in decomposition processes is a key problem of HHT. A new technique based on response surface method (RSM), which establishes the recursive relations between sample points of signals, is presented to deal with this difficult problem. Besides, the boundary extension problem arising from HHT can be described by mathematical least squares problem but traditional gradient algorithms may diverge when the Hessian matrix of the object function of the least squares problem is non-positive. It has been proved that the generalized inverse of the linear equations (derived from the linear least squares problem) by singular value decomposition is the solution of original linear least squares problems. Thereby the divergence problem is also solved. Analysis results with respect to simulation signals and measured signals show that the method with new boundary extension technique performs successfully for HHT.

scholarly journals A Weighted Linear Least Squares Location Method of an Acoustic Emission Source without Measuring Wave Velocity

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3191 ◽  
Author(s):  
Zilong Zhou ◽  
Yichao Rui ◽  
Xin Cai ◽  
Ruishan Cheng ◽  
Xueming Du ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Least Squares ◽  
Wave Velocity ◽  
Linear Equations ◽  
Linear Least Squares ◽  
Governing Equations ◽  
Traditional Methods ◽  
Location Method ◽  
Reference Equation ◽  
The Mean

The location of an acoustic emission (AE) source is crucial for predicting and controlling potential hazards. In this paper, a novel weighted linear least squares location method for AE sources without measuring wave velocity is proposed. First, the governing equations of each sensor are established according to the sensor coordinates and arrival times. Second, a mean reference equation is established by taking the mean of the squared governing equations. Third, the system of linear equations can be obtained based on the mean reference equation, and their residuals are estimated to obtain their weights. Finally, the AE source coordinate is obtained by weighting the linear equations and inserting the parameter constraint. The AE location method is verified by a pencil lead break experiment, and the results show that the locating accuracy of the proposed method is significantly higher than that of traditional methods. Furthermore, the simulation test proves that the proposed method also has a better performance (location accuracy and stability) than the traditional methods under any given scale of arrival errors.

Utilisation of pressure-volume techniques and non-linear least squares analysis to investigate site induced stresses in evergreen trees

Oecologia ◽  
1983 ◽  
Vol 57 (3) ◽  
pp. 380-390 ◽  
Author(s):  
G. T. Jane ◽  
T. G. A. Green
Keyword(s):  
Least Squares ◽  
Linear Least Squares ◽  
Non Linear ◽  
Induced Stresses

scholarly journals Adaptive Robust Kernels for Non-Linear Least Squares Problems

2021 ◽  
pp. 1-1
Author(s):  
Nived Chebrolu ◽  
Thomas Labe ◽  
Olga Vysotska ◽  
Jens Behley ◽  
Cyrill Stachniss
Keyword(s):  
Least Squares ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Non Linear ◽  
Linear Least Squares Problems
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