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Solving bilinear tensor least squares problems and application to Hammerstein identification
Author(s) -
Eldén Lars,
AhmadiAsl Salman
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2226
Subject(s) - bilinear interpolation , mathematics , least squares function approximation , non linear least squares , constraint (computer aided design) , nonlinear system , tensor (intrinsic definition) , projection (relational algebra) , mathematical optimization , gauss , identification (biology) , projection method , separable space , algorithm , mathematical analysis , estimation theory , dykstra's projection algorithm , estimator , geometry , statistics , physics , botany , quantum mechanics , biology
Summary Bilinear tensor least squares problems occur in applications such as Hammerstein system identification and social network analysis. A linearly constrained problem of medium size is considered, and nonlinear least squares solvers of Gauss–Newton‐type are applied to numerically solve it. The problem is separable, and the variable projection method can be used. Perturbation theory is presented and used to motivate the choice of constraint. Numerical experiments with Hammerstein models and random tensors are performed, comparing the different methods and showing that a variable projection method performs best.