CSC_349_HANDOUT#24

CSC_349_HANDOUT#24 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 24 CUBIC SPLINE INTERPOLANTS The following definition is the same as given in points 1-5 on pages 501-502 of the 5 th ed. (pages 515-516 of the 6 th ed.), but is more precise. Definition Given data < + , ) ( , ), ( ), ( and , with , , , 1 0 1 1 0 n i i n x f x f x f x x x x x K K S ( x ) is a cubic spline interpolant for ) ( x f if (a) S ( x ) is a cubic polynomial, denoted by S j ( x ) , on each subinterval 1 0 , ] , [ 1 + n j x x j j (b) ) ( ) ( j j j x f x S = , for 1 0 n j and ) ( ) ( 1 n n n x f x S = (c) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j (d) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j (e) ) ( ) ( 1 1 1 + + + = j j j j x S x S , for 2 0 n j and (f ) either one of the following hold: (i) S ( x 0 ) =′ S ( x n ) = 0 --- the free or natural boundary conditions or (ii) ) ( ) ( 0 0 x f x S = and ) ( ) ( n n x f x S = ---
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CSC_349_HANDOUT#24 - COMPUTER SCIENCE 349A Handout Number...

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