-regularly varying functions in approximation theory.
A best approximation property of the generalized spline functions.
A characterization of random approximations.
A characterization of strictly convex metric linear spaces.
A Continuous Selection of the Metric Projection in Matrix Spaces, Addendum.
A counterexample in comonotone approximation in space
Refining the idea used in [24] and employing very careful computation, the present paper shows that for 0 < p ≤ ∞ and k ≥ 1, there exists a function , with for x ∈ [0,1] and for x ∈ [-1,0], such that lim supn→∞ (en(k)(f)p) / (ωk+2+[1/p](f,n-1)p) = + ∞ where is the best approximation of degree n to f in by polynomials which are comonotone with f, that is, polynomials P so that for all x ∈ [-1,1]. This theorem, which is a particular case of a more general one, gives a complete solution...
A descent algorithm for - approximation of continuous functions with values in unitary space
A Discrepancy Theorem Concerning Polynomials of Best Approximation in L...[-1, 1].
A fast iteration for uniform approximation
The paper gives such an iterative method for special Chebyshev approxiamtions that its order of convergence is . Somewhat comparable results are found in [1] and [2], based on another idea.
A moment problem for discrete nonpositive measures on a finite interval.
A non-Chebyshev finite-dimensional subspace in
A note on Chebyshev centres
A note on f-best approximation in reflexive Banach spaces
A remark on uniqueness of best rational approximants of degree 1 in of the circle.
A Remez Type Algorithm for Spline Functions
A structural theorem of the generalized spline functions.
Adaptive convex optimization in Banach spaces: a multilevel approach
This is mainly a review paper, concerned with some applications of the concept of Nonlinear Approximation to adaptive convex minimization. At first, we recall the basic ideas and we compare linear to nonlinear approximation for three relevant families of bases used in practice: Fourier bases, finite element bases, wavelet bases. Next, we show how nonlinear approximation can be used to design rigorously justified and optimally efficient adaptive methods to solve abstract minimization problems in...
Alternation for Best Spline Approximations
An Algorithm for Segment Approximation.
An analogue of Montel’s theorem for some classes of rational functions
For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best -approximation with an unbounded number of finite poles are considered.