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Given a tensor in some canonical representation, we consider a problem
of approximation with a fixed number of summands. To solve this problem,
one can naturally try to adopt some general minimization techniques.
One successful method in this line was recently proposed by M.Espig.
This talk contributes to the same line in the two ways.
First, we discover a more detailed structure in the Hessian and show
that all auxiliary matrices of quadratic model can be obtained with the
cost quadratic in the dimensionality (instead of cubic in the previous
works).
Second, we develop a successful version of a Newton Trust Region-based
algorithm. This algorithm effectively exploits stucture of the Hessian
to minimize the objective function. To solve the Newton minimization
problem with trust-region constraints at each step, we use the
preconditioned conjugate gradients. When the Hessian becomes indefinite,
we apply the strategy proposed by Steihaug. Convergence to a local
minimum is global superlinear and local quadratic.
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