scholarly journals Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

2020 ◽  
pp. 1-1 ◽  
Author(s):  
Zheng Dang ◽  
Kwang Moo Yi ◽  
Yinlin Hu ◽  
Fei Wang ◽  
Pascal Fua ◽  
...  
Keyword(s):  
Least Square ◽  
Deep Networks ◽  
Linear Least Square ◽  
Least Square Problems

scholarly journals Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Yanli Du ◽  
Fuping Tan
Keyword(s):  
Least Squares ◽  
Least Square ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Numerical Example ◽  
Comparison Results ◽  
Linear Least Squares Problems ◽  
Linear Least Square ◽  
Least Square Problems ◽  
Theoretical Results

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerical example to confirm our theoretical results.

scholarly journals Application of a Sparsity Pattern and Region Clustering for Near Field Sparse Approximate Inverse Preconditioners in Method of Moments Simulations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Carlos Delgado ◽  
Javier Moreno ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Near Field ◽  
Least Square ◽  
Approximate Inverse ◽  
Sparsity Pattern ◽  
Field Coupling ◽  
Sparse Approximate Inverse ◽  
Coupling Terms ◽  
Linear Least Square ◽  
Least Square Problems

This document presents a technique for the generation of Sparse Inverse Preconditioners based on the near field coupling matrices of Method of Moments simulations where the geometry has been partitioned in terms of regions. A distance parameter is used to determine the sparsity pattern of the preconditioner. The rows of the preconditioner are computed in groups at a time, according to the number of unknowns contained in each region of the geometry. Two filtering thresholds allow considering only the coupling terms with a significant weight for a faster generation of the preconditioner and storing only the most significant preconditioner coefficients in order to decrease the memory required. The generation of the preconditioner involves the computation of as many independent linear least square problems as the number of regions in which the geometry is partitioned, resulting in very good scalability properties regarding its parallelization.

GPS-DERIVED SECULAR VELOCITY FIELD AROUND SANGIHE ISLAND AND ITS IMPLICATION TO THE MOLUCCA SEA SEISMICITY

GEOMATIKA ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 107
Author(s):  
Leni Sophia Heliani ◽  
Cecep Pratama ◽  
Parseno Parseno ◽  
Nurrohmat Widjajanti ◽  
Dwi Lestari
Keyword(s):  
Surface Displacement ◽  
Active Regions ◽  
Least Square ◽  
The Other ◽  
Gps Data ◽  
West Side ◽  
Active Deformation ◽  
Secular Motion ◽  
Small Change ◽  
Linear Least Square

<p><em>Sangihe-Moluccas region is the most active seismicity in Indonesia. Between 2015 to 2018 there is four M6 class earthquake occurred close to the Sangihe-Moluccas region. These seismic active regions representing active deformation which is recorded on installed GPS for both campaign and continuous station. However, the origin of those frequent earthquakes has not been well understood especially related to GPS-derived secular motion. Therefore, we intend to estimate the secular motion inside and around Sangihe island. On the other hand, we also evaluate the effect of seismicity on GPS sites. Since our GPS data were conducted on yearly basis, we used an empirical global model of surface displacement due to coseismic activity. We calculate the offset that may be contained in the GPS site during its period</em><em>. </em><em>We remove the offset and estimate again the secular motion using linear least square. Hence, in comparison with the secular motion without considering the seismicity, we observe small change but systematically shifting the motion. We concluded the seismicity in the Molucca sea from 2015 to 2018 systematically change the secular motion around Sangihe Island at the sub-mm level. Finally, we obtained the secular motion toward each other between the east and west side within 1 to 5.5 cm/year displacement. </em></p>

scholarly journals An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 920
Author(s):  
Neha Chaudhary ◽  
Othman Isam Younus ◽  
Luis Nero Alves ◽  
Zabih Ghassemlooy ◽  
Stanislav Zvanovec ◽  
...  
Keyword(s):  
Visible Light ◽  
Polynomial Regression ◽  
Power Level ◽  
Least Square ◽  
Line Of Sight ◽  
Received Power ◽  
Strength Based ◽  
Complex Linear ◽  
Linear Least Square ◽  
First Time

The accuracy of the received signal strength-based visible light positioning (VLP) system in indoor applications is constrained by the tilt angles of transmitters (Txs) and receivers as well as multipath reflections. In this paper, for the first time, we show that tilting the Tx can be beneficial in VLP systems considering both line of sight (LoS) and non-line of sight transmission paths. With the Txs oriented towards the center of the receiving plane (i.e., the pointing center F), the received power level is maximized due to the LoS components on F. We also show that the proposed scheme offers a significant accuracy improvement of up to ~66% compared with a typical non-tilted Tx VLP at a dedicated location within a room using a low complex linear least square algorithm with polynomial regression. The effect of tilting the Tx on the lighting uniformity is also investigated and results proved that the uniformity achieved complies with the European Standard EN 12464-1. Furthermore, we show that the accuracy of VLP can be further enhanced with a minimum positioning error of 8 mm by changing the height of F.

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

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