Approximations in $L^p $ and Chebyshev Approximations

The Limit of Best Generalized Peak Norm Approximations

“…THE CASE α → 0 Now we consider the situation when α → 0+. It appears necessary to impose stronger conditions on the problem to get results equivalent to those of Theorems 1 and 2, and it is interesting that this in a sense reflects what happens in other analogous cases (for example, [4,6]). We begin with the following definition.…”

The Chebyshev solution of the linear matrix equationAX+YB=C

“…Therefore, there exists a nonzero number ej such that We now reformulate necessary and sufficient condition (see Theorem 3.1) for the Chebyshev solution of (1.1) under the assumptions (1.6) and give a formula for 6~o. Then, we shall apply these conditions to determine the characteristic set of AX + YB = C (see [6] (3.10) where wi, uj and ~ are given in (3.1) and (3.2), respectively. Moreover, 6~=1~1.…”

Rate of Convergence of the Linear Discrete Polya Algorithm

“…The Polya algorithm is an attempt to define h* as the limit of the best p-approximation h p as p Ä . If K is an affine subspace of R n , then the Polya algorithm converges to the strict uniform approximation [1,4,5],…”