Chebyshev Approximation with the Local Haar Condition
Charles B. Dunham · SIAM Journal on Numerical Analysis · 1971
Chebyshev approximation by nonlinear families on a general compact space is studied. Attention is restricted to approximants satisfying a local Haar condition. A necessary and sufficient condition for the approximant to be locally best is given. A linear approximation problem is given which is equivalent to the nonlinear problem of locally best approximation. The existence of a minimal set on which a locally best approximation is locally best is shown. An alternation result is given for approximation on an interval.