Simultaneous approximation and interpolation inL1andC(T)

Lambert, Joseph M.

doi:10.2140/pjm.1973.45.293

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1974

1976

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Cited by 4 publications

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“…(See [2] for references.) Also Lambert [4] has studied property SAIN for L, and C(77), and Holmes and Lambert [3] studied the property SAIN from a geometrical point of view. Proceeding with the proof, let/ G C[a,£] be given along with interpolation points {t,},= 1 and e > 0.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Spline Approximation and Interpolation Preserving Norms

Chui¹,

Rozema²,

Smith³

et al. 1976

Proceedings of the American Mathematical Society

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Abstract.In this paper, it is proved that splines of order k (k > 2) have property SAIN. The proof of this result is based on the important properties of B-splines. Introduction.In a recent manuscript [5], Lambert proved that the twice continuously differentiable cubic splines possess property SAIN (simultaneous approximation and interpolation which is norm preserving) on C [a, b] where the interpolatory constraints are point evaluations. In this paper we establish the more general result for splines of any order greater than 1 while at the same time supplying a simple proof. More precisely, we will show

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Section: Introductionmentioning

confidence: 99%