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CSC_349_HANDOUT#25 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 25 CUBIC SPLINE INTERPOLATION Example : the case n = 3. o o o o S (x) 0 S (x) S (x) 1 2 h 0 h 1 h 2 x 0 x 1 x 2 x 3 o denotes interpolated values f(x ) i Condition (b) in the definition of a cubic spline interpolant implies that ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 3 3 2 2 2 2 1 1 1 0 0 0 x f x S x f x S x f x S x f x S = = = = Condition (c) implies that ) ( ) ( above from or ) ( ) ( ) ( ) ( above from or ) ( ) ( 2 1 2 2 1 2 2 1 0 1 1 0 1 1 x S x f x S x S x S x f x S x S = = = = Condition (d) implies that S 1 ( x 1 ) = S 0 ( x 1 ) S 2 ( x 2 ) = S 1 ( x 2 ) Condition (e) implies that S 1 ( x 1 ) = S 0 ( x 1 ) S 2 ( x 2 ) = ′′ S 1 ( x 2 )
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