Fast singular-value decomposition of Loewner matrices for state-space macromodeling

2015 ◽  
Author(s):  
Amit Hochman
Keyword(s):  
Singular Value Decomposition ◽  
State Space ◽  
Singular Value ◽  
Value Decomposition

scholarly journals Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

2021 ◽  
Vol 9 (7) ◽  
pp. 768
Author(s):  
Romain Lecuyer-Le Bris ◽  
Marc Le Boulluec ◽  
Jean-Frédéric Charpentier ◽  
Mohamed Benbouzid
Keyword(s):  
Singular Value Decomposition ◽  
State Space ◽  
Kernel Function ◽  
State Space Model ◽  
Hankel Matrix ◽  
Singular Value ◽  
Radiation Forces ◽  
Function Definition ◽  
Definition Of ◽  
Value Decomposition

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

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