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Author
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2024
Vol. 1
no. 1
Vol. 2
2023
Vol. 1
no. 1
no. 2
2022
Vol. 1
no. 1
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Vol. 1
no. 1
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Vol. 2
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Vol. 2
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no. 2
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Vol. 0
Vol. 1
PARAFAC Identification of Higher Order Volterra Kernels
Pages
:
48-54
Nabiha Saidi, Hassani Messaoud
Volterra series are used to model a large class of non linear systems. The resulting model which is linear with respect to its parameters, suffers from the high number of these parameters which bereaves its use in real time applications. To reduce this complexity we assume that the high order kernels can be described by tensors which may be split into two-dimensions matrices. The splitting operation is due to PARAFAC (PARAllel FACtor) decomposition and the matrix components identification is accomplished by an Alternating Least Square (ALS) technique.In this paper we detail the identification of the PARAFAC decomposition of third order Volterrakernels. For higher order we reduce in a first step the corresponding tensor to a third order one for which we identify the three matrices components using ALS algorithm. Then we use the Singular ValueDecomposition (SVD) to determine all the matrices of the PARAFAC decomposition of higher order kernel.
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