Optimal spline spaces for $L^2$ $n$-width problems with boundary conditions

Espen Sande; Michael S. Floater

arxiv: 1709.02710 · v4 · pith:2ZUVYJLXnew · submitted 2017-09-08 · 🧮 math.NA · cs.NA· math.CA

Optimal spline spaces for L² n-width problems with boundary conditions

Michael S. Floater , Espen Sande This is my paper

classification 🧮 math.NA cs.NAmath.CA

keywords spacessplineboundaryconditionsoptimaladmitcertainclasses

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In this paper we show that, with respect to the $L^2$ norm, three classes of functions in $H^r(0,1)$, defined by certain boundary conditions, admit optimal spline spaces of all degrees $\geq r-1$, and all these spline spaces have uniform knots.

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Optimal spline spaces for L² n-width problems with boundary conditions

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