scholarly journals Sparse estimation from noisy observations of an overdetermined linear system

Automatica ◽  
2014 ◽  
Vol 50 (11) ◽  
pp. 2845-2851 ◽  
Author(s):  
Liang Dai ◽  
Kristiaan Pelckmans
Keyword(s):  
Linear System ◽  
Sparse Estimation ◽  
Overdetermined Linear System

scholarly journals An overdetermined linear system

1976 ◽  
Vol 18 (3) ◽  
pp. 264-277 ◽  
Author(s):  
Michael L Levitan ◽  
Roger Y.S Lynn
Keyword(s):  
Linear System ◽  
Overdetermined Linear System

scholarly journals Factored solution of nonlinear equation systems

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140236 ◽  
Author(s):  
Antonio Gómez-Expósito
Keyword(s):  
Linear System ◽  
Large Scale ◽  
Symmetric Matrix ◽  
Solution Process ◽  
Nonlinear Systems Of Equations ◽  
Large Scale Systems ◽  
Augmented System ◽  
Step Procedure ◽  
Nonlinear Equation Systems ◽  
Overdetermined Linear System

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton–Raphson scheme. The original nonlinear system is first unfolded into three simpler components: (i) an underdetermined linear system, (ii) a one-to-one nonlinear mapping with explicit inverse, and (iii) an overdetermined linear system. Then, instead of solving such an augmented system at once, a two-step procedure is proposed in which two equation systems are solved at each iteration, one of them involving the same symmetric matrix throughout the solution process. The resulting factored algorithm converges faster than Newton's method and, if carefully implemented, can be computationally competitive for large-scale systems. It can also be advantageous for dealing with infeasible cases.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Impossibility of steady squeezing for two-mode linear system without self-action

1991 ◽  
Vol 1 (9) ◽  
pp. 1217-1227 ◽  
Author(s):  
A. A. Bakasov ◽  
N. V. Bakasova ◽  
E. K. Bashkirov ◽  
V. Chmielowski
Keyword(s):  
Linear System
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