scholarly journals Root Radii and Subdivision for Polynomial Root-Finding

2021 ◽  
pp. 136-156
Author(s):  
Rémi Imbach ◽  
Victor Y. Pan
Keyword(s):  
Root Finding ◽  
Polynomial Root Finding

scholarly journals DoA Estimation Using Neural Tangent Kernel under Electromagnetic Mutual Coupling

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1057
Author(s):  
Qifeng Wang ◽  
Xiaolin Hu ◽  
Xiaobao Deng ◽  
Nicholas E. Buris
Keyword(s):  
Mutual Coupling ◽  
Deep Neural Network ◽  
Doa Estimation ◽  
Antenna Element ◽  
Root Finding ◽  
Multiple Signal ◽  
Estimation Problems ◽  
Limiting Case ◽  
Signal Doa Estimation ◽  
Polynomial Root Finding

Antenna element mutual coupling degrades the performance of Direction of Arrival (DoA) estimation significantly. In this paper, a novel machine learning-based method via Neural Tangent Kernel (NTK) is employed to address the DoA estimation problem under the effect of electromagnetic mutual coupling. NTK originates from Deep Neural Network (DNN) considerations, based on the limiting case of an infinite number of neurons in each layer, which ultimately leads to very efficient estimators. With the help of the Polynomial Root Finding (PRF) technique, an advanced method, NTK-PRF, is proposed. The method adapts well to multiple-signal scenarios when sources are far apart. Numerical simulations are carried out to demonstrate that this NTK-PRF approach can handle, accurately and very efficiently, multiple-signal DoA estimation problems with realistic mutual coupling.

scholarly journals Efficient high degree polynomial root finding using GPU

2017 ◽  
Vol 18 ◽  
pp. 46-56 ◽  
Author(s):  
Kahina Ghidouche ◽  
Abderrahmane Sider ◽  
Raphaël Couturier ◽  
Christophe Guyeux
Keyword(s):  
Degree Polynomial ◽  
Root Finding ◽  
High Degree ◽  
Polynomial Root Finding

Polynomial root-finding via structured matrices

2013 ◽  
Vol 46 (3/4) ◽  
pp. 118-119
Author(s):  
Esteban Segura Ugalde
Keyword(s):  
Structured Matrices ◽  
Root Finding ◽  
Polynomial Root Finding

scholarly journals Backward stability of polynomial root-finding using Fiedler companion matrices

2015 ◽  
pp. dru057 ◽  
Author(s):  
Fernando de Terán ◽  
Froilán M. Dopico ◽  
Javier Pérez
Keyword(s):  
Root Finding ◽  
Backward Stability ◽  
Companion Matrices ◽  
Polynomial Root Finding

Polynomial root finding technique for joint DOA DOD estimation in bistatic MIMO radar

2010 ◽  
Vol 90 (9) ◽  
pp. 2723-2730 ◽  
Author(s):  
Mohamed Laid Bencheikh ◽  
Yide Wang ◽  
Hongyang He
Keyword(s):  
Mimo Radar ◽  
Bistatic Mimo Radar ◽  
Root Finding ◽  
Polynomial Root Finding

scholarly journals Matrix computations and polynomial root-finding with preprocessing

2011 ◽  
Vol 434 (4) ◽  
pp. 854-879 ◽  
Author(s):  
Victor Y. Pan ◽  
Guoliang Qian ◽  
Ai-Long Zheng ◽  
Zhao Chen
Keyword(s):  
Matrix Computations ◽  
Root Finding ◽  
Polynomial Root Finding

Polynomial root-finding with matrix eigen-solving

2005 ◽  
Vol 39 (3) ◽  
pp. 87-87
Author(s):  
Victor Pan
Keyword(s):  
Root Finding ◽  
Polynomial Root Finding

scholarly journals Polynomial Root-Finding Algorithms and Branched Covers

1994 ◽  
Vol 23 (2) ◽  
pp. 415-436 ◽  
Author(s):  
Myong-Hi Kim ◽  
Scott Sutherland
Keyword(s):  
Branched Covers ◽  
Root Finding ◽  
Polynomial Root Finding
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