6 research outputs found
Nonlinear tensor product approximation of functions
We are interested in approximation of a multivariate function
by linear combinations of products
of univariate functions , . In the case it is a
classical problem of bilinear approximation. In the case of approximation in
the space the bilinear approximation problem is closely related to the
problem of singular value decomposition (also called Schmidt expansion) of the
corresponding integral operator with the kernel . There are known
results on the rate of decay of errors of best bilinear approximation in
under different smoothness assumptions on . The problem of multilinear
approximation (nonlinear tensor product approximation) in the case is
more difficult and much less studied than the bilinear approximation problem.
We will present results on best multilinear approximation in under mixed
smoothness assumption on