Discrete spline interpolation: Difference between revisions

Revision as of 23:14, 12 December 2016

Revision as of 15:31, 14 May 2018

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:<math>D^{(j)}g_{i+1}(x_i)=D^{(j)}g_i(x_i) \text{ for } j=0,1,2 \text{ and } i=1,2, \ldots, n-1.</math>

This states that the central differences <math>D^{(j)}g(x)</math> are continuous at ''x''_''i''.

===Example===

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:<math>D^{(1)}g_n(x_n) = D^{(1)}f(x_n).</math>

This unique discrete cubic spline is the discrete spline interpolant to ''f''(''x'') in the interval [''x''₀ - h, ''x''_{''n_''} + h]. This interpolant agrees with the values of ''f''(''x'') at ''x''₀, ''x''₁, . . ., ''x''_n.

==Applications==