$C^2$ Interpolation with Range Restriction

Abstract

) is within a constant multiple of the least possible, with the constant depending only on m and n? In this paper, we provide the solution to the problem for the case m = 2. Specifically, we construct a (parameter-dependent, nonlinear) C 2 (R n ) extension operator that preserves the range [λ, Λ], and we provide an efficient algorithm to compute such an extension using O(N log N) operations, where N = #(E).