The (In)Complete Compendium of Computational Curiosities: Givens' Rotations.

1995 ◽  
Author(s):  
Carlos F. Borges
Keyword(s):  
Givens Rotations

scholarly journals Blind Source Separation Algorithms Using Hyperbolic and Givens Rotations for High-Order QAM Constellations

2018 ◽  
Vol 66 (7) ◽  
pp. 1802-1816 ◽  
Author(s):  
Syed Awais Wahab Shah ◽  
Karim Abed-Meraim ◽  
Tareq Y. Al-Naffouri
Keyword(s):  
Blind Source Separation ◽  
Source Separation ◽  
High Order ◽  
Givens Rotations

scholarly journals Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

2021 ◽  
Vol 1 (1) ◽  
pp. 58-62
Author(s):  
Ammar Mesloub
Keyword(s):  
Complex Case ◽  
Eigenvalue Decomposition ◽  
Real Case ◽  
Joint Diagonalization ◽  
The Real ◽  
Givens Rotation ◽  
Givens Rotations ◽  
Simulation Results ◽  
Complex Joint

This paper shows the different ways of using generalized Givens rotations in complex joint eigenvaluedecomposition (JEVD) problem. It presents the different schemes of generalized Givens rotation, justifies the introducedapproximations and focuses on the process of extending an algorithm developed for real JEVD to the complex JEVD.Several Joint Diagonalization problem use generalized Givens rotations to achieve the solution, many algorithmsdeveloped in the real case exist in the literature and are not generalized to the complex case. Hence, we show herein asimple and not trivial way to get the complex case from the real one. Simulation results are provided to highlight theeffectiveness and behaviour of the proposed techniques for different scenarios.

scholarly journals Simple Orbit Determination Using GPS Based on a Least-Squares Algorithm Employing Sequential Givens Rotations

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Rodolpho Vilhena de Moraes ◽  
Aurea Aparecida da Silva ◽  
Helio Koiti Kuga
Keyword(s):  
Least Squares ◽  
Orbit Determination ◽  
Least Squares Method ◽  
Artificial Satellite ◽  
Low Cost ◽  
Recursive Least Squares ◽  
Gps Receiver ◽  
Gravity Field Model ◽  
Givens Rotations ◽  
Recursive Least Squares Method

A low-cost computer procedure to determine the orbit of an artificial satellite by using short arc data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens rotations for solving recursive and sequential orbit determination problems. To assess the procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model, was considered. When compared with the reference Precision Orbit Ephemeris (POE) of JPL/NASA, the results have indicated that precision better than 9 m is easily obtained, even when short batches of data are used.

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