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Unformatted text preview: + 1 ∞ X j = i N k +1 j ( u ). If k = 1, the relations in (b) and (c) holds for all u except for the knots. ( ? points ) 8.3. Consider the class of functions on [ a, b ], which are summable with square of its second derivative, W 2 2 [ a, b ]. Consider interpolate function u ( x ) ∈ W 2 2 [ a, b ] , u ( x i ) = f ( x i ) i = 0 , 1 , . . . , n, which minimizes the functional J ( u ) = Z b a ² d 2 u dx 2 ³ 2 dx. Show that such function is natural cubic spline. ( 10 points ) Due: 16.04.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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- Spring '10