Discrete spline interpolation: Difference between revisions

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In the mathematical field of [[numerical analysis]], '''discrete spline interpolation''' is a form of [[interpolation]] where the [[interpolant]] is a special type of [[piecewise]] [[polynomial]] called a discrete spline. A discrete spline is a piecewise polynomial such that its [[central difference]]s are [[Continuous function|continuous]] at the knots whereas a [[Spline (mathematics)|spline]] is a piecewise polynomial such that its [[derivative]]s are continuous at the knots. Discrete cubic splines are discrete splines where the central differences of orders 0, 1, and 2 are required to be continuous.<ref name=Tom>{{cite journal|last1=Tom Lyche|title=Discrete Cubic Spline Interpolation|journal=BIT|date=1979|volume=16|pages=281–290|doi=10.1007/bf01932270}}</ref>

Discrete splines were introduced by Mangasarin and Schumaker in 1971 as solutions of certain minimization problems involving differences.<ref name=Mangasarin>{{cite journal|last1author1=Mangasarian, O. L. and |author2=Schumaker, L. L.|title=Discrete splines via mathematical programming|journal=SIAM J. Control.|date=1971|volume=9|pages=174–183|doi=10.1137/0309015}}</ref>

==Discrete cubic splines==