B. Mulansky and M. Neamtu, Interpolation and approximation from convex sets, J. Approx. Theory, 92(1998), 82--100. Home/Search Document Details and Download
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Convex Preserving Scattered Data Interpolation Using Bivariate .. - Lai (2004) (1 citation) (Correct)
.... Theta 304 2007s 10153s 9156s 81 387 Theta 387 4276s 33112s 24107s 100 480 Theta 480 11559s too long too long Acknowledgment: The author would like to thank Professor Larry L. Schumaker for a helpful discussion on the convexity preserving interpolation problem, M. Neamtu for providing his paper [12] and Paul Wenston for helpful assistance in implementing these three LCQP methods. ....
B. Mulansky and M. Neamtu, Interpolation and approximation from convex sets, J. Approx. Theory, 92(1998), 82--100.
Interpolation and Approximation from Convex Sets II.. - Bernd Mulansky.. (1998) (2 citations) Self-citation (Mulansky Neamtu) (Correct)
....is sometimes also coined shape preserving interpolation. If problem (1) has a solution for a given data point d, we say that d is admissible. Clearly, this means that d 2 A[C] fAx : x 2 Cg, or equivalently C A Gamma1 (d) 6= where A Gamma1 (d) fx 2 X : Ax = dg : In [8] we studied the problem of solvability of constrained interpolation when the set C is replaced by a convex subset B of C. In this case the constrained interpolation problem consists in finding an element x from X such that x 2 B A Gamma1 (d) Frequently, B is given as the intersection of C ....
....For example, if C is a set of monotone functions, B could be the set of all strictly monotone functions in C. It is clear that even if d admits interpolation from C, it may not admit interpolation from B. However, under the assumptions that Y is finite dimensional and B dense in C, we proved in [8] that each interior data point d 2 int(A[C] admits interpolation from B and that in fact B A Gamma1 (d) is dense in C A Gamma1 (d) Below, in Section 2, we present new proofs of this result. The unifying approach introduced in the above cited paper has many interesting applications in ....
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B. Mulansky and M. Neamtu, Interpolation and approximation from convex sets, J. Approx. Theory 92, 82--100, 1998.
Convexity Preserving Interpolation By Dual Subdivision.. - Ilana Johanna Wartenberg (1998) (Correct)
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B. Mulansky, M. Neamtu, Interpolation and Approximation from Convex Sets, Journal of Approximation Theory, Vol. 92, No. 1, January 1998.
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