Differential equations for the analytic singular value decomposition of a matrix

1992 ◽  
Vol 63 (1) ◽  
pp. 283-295 ◽  
Author(s):  
K. Wright
Keyword(s):  
Singular Value Decomposition ◽  
Differential Equations ◽  
Singular Value ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

scholarly journals Optimal Attitude Determination from Vector Sensors Using Fast Analytical Singular Value Decomposition

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Zhuohua Liu ◽  
Wei Liu ◽  
Xiangyang Gong ◽  
Jin Wu
Keyword(s):  
Singular Value Decomposition ◽  
Attitude Determination ◽  
Computation Time ◽  
Singular Value ◽  
Simulation Experiments ◽  
Vector Sensors ◽  
Vector Observation ◽  
Wahba Problem ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

A novel algorithm is proposed in this paper to solve the optimal attitude determination formulation from vector observation pairs, that is, the Wahba problem. We propose here a fast analytic singular value decomposition (SVD) approach to obtain the optimal attitude matrix. The derivations and mandatory proofs are presented to clarify the theory and support its feasibility. Through simulation experiments, the proposed algorithm is validated. The results show that it maintains the same attitude determination accuracy and robustness with conventional methodologies but significantly reduces the computation time.

Singular-value decomposition method in atomic scattering

2003 ◽  
Vol 81 (10) ◽  
pp. 1215-1221 ◽  
Author(s):  
E Zerrad ◽  
A -S Khan ◽  
K Zerrad ◽  
G Rawitscher
Keyword(s):  
Wave Function ◽  
Phase Shift ◽  
Singular Value Decomposition ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Kernel ◽  
Singular Value ◽  
Singular Value Decomposition Method ◽  
Atomic Scattering ◽  
Value Decomposition

A new numerical method for solving the integro-differential equations that appear in the theory of atomic scattering is devised. It consists of decomposing the kernel into separable terms via the method of singular-value decomposition. A set of integro-differential equations involving the residual integral kernel are then solved to obtain the wave function and from this the phase shift is evaluated. PACS Nos.: 23.23.+x, 56.65.DY

Numerical computation of an analytic singular value decomposition of a matrix valued function

1991 ◽  
Vol 60 (1) ◽  
pp. 1-39 ◽  
Author(s):  
Angelika Bunse-Gerstner ◽  
Ralph Byers ◽  
Volker Mehrmann ◽  
Nancy K. Nichols
Keyword(s):  
Singular Value Decomposition ◽  
Numerical Computation ◽  
Singular Value ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

Analytic singular value decomposition of a channeled spectropolarimeter

2001 ◽  
Author(s):  
Derek S. Sabatke ◽  
A.M. Locke ◽  
M.R. Descour ◽  
J.P. Garcia ◽  
E.L. Dereniak ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition
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