Uniqueness in one-sided linear Chebyshev approximation

Discrete linear Chebyshev approximation

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One-Sided Approximation of Functions

where :Yl denotes the orthogonal complement of Y (see [I]). Another example of this type of duality appears in one of the classical moment problems. Letfbe Bore1 measurable and bounded on [a,b], h,, . . ., h, a CebySev system on [a,b] and for a given positive Bore1 measure yO defined on [a,b] denote by C (y,,) the class of all positive Bore1 measures y which satisfy f.bhkdy=[hkdyo k= 1,2 ,..., ...

On One-Sided Ideals of Rings of Linear Transformations

One-sided approximation by entire functions

Let f : R→ R have an nth derivative of finite variation Vf(n) and a locally absolutely continuous (n− 1)st derivative. Denote by E±(f, δ)p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in Lp(R)–norm. For 1 ≤ p ≤ ∞ we show the estimate E±(f, δ)p ≤ C n π1/pVf(n)δ −n− 1 p , with constants Cn > 0.

Computation of Best One - Sided Lx Approximation

A computational procedure based on linear programming is presented for finding the best one-sided Li approximation to a given function. A theorem which ensures that the computational procedure yields approximations which converge to the best approximation is proved. Some numerical examples are discussed.