Characterization and uniqueness of best uniform vector-valued linear approximation

Uniform Approximation of Vector-Valued Functions with a Constraint

This paper deals with existence and characterization of best approximations to vector-valued functions. The approximations are themselves vector-valued functions with components taken from a linear space, but the constraint is imposed that certain of the approximation parameters should be identical for all components.

The Number of Singular Vector Tuples and Uniqueness of Best Rank-One Approximation of Tensors

In this paper we discuss the notion of singular vector tuples of a complex valued d-mode tensor of dimension m1 × . . . × md. We show that a generic tensor has a finite number of singular vector tuples, viewed as points in the corresponding Segre product. We give the formula for the number of singular vector tuples. We show similar results for tensors with partial symmetry. We give analogous re...

Some Results on p-Best Approximation in Vector Spaces

Behavior of Polynomials of Best Uniform Approximation

We investigate the asymptotic behavior of the polynomials {Pn(f)}'t' of best uniform approximation to a function f that is continuous on a compact set K of the complex plane C and analytic in the interior of K, where K has connected complement. For example, we show that for "most" functions f, the error f -Pn(f) does not decrease faster at interior points of K than on K itself. We also describe...

Best approximation by integer-valued functions

Given an integer function f , the problem is to find its best uniform approximation from a set K of integervalued bounded functions. Under certain conditions on K , the best extremal (maximal or minimal) approximation is identified. Furthermore, the operator mapping f to its extremal best approximation is shown to be Lipschitzian with some constant C or optimal Lipschitzian having the smallest ...