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Unformatted text preview: Cubic Splines James Keesling 1 Definition of Cubic Spline Given a function f ( x ) defined on an interval [ a,b ] we want to fit a curve through the points { ( x ,f ( x )) , ( x 1 ,f ( x 1 )) ,..., ( x n ,f ( x n )) } as an approximation of the function f ( x ). We assume that the points are given in order a = x < x 1 < x 2 < ··· < x n = b and let h i = x i +1 x i . The method of approximation we describe is called cubic spline interpolation . The cubic spline is a function S ( x ) on [ a,b ] with the following properties. S ( x ) [ x i ,x i +1 ] = S i ( x ) is a cubic polynomial for i = 0 , 1 , 2 ,...,n 1 S i ( x i ) = f ( x i ) for i = 0 , 1 , 2 ,...,n 1 S i ( x i +1 ) = f ( x i +1 ) for i = 0 , 1 , 2 ,...,n 1 S i ( x i +1 ) = S i +1 ( x i +1 ) for i = 0 , 1 , 2 ,...,n 2 S 00 i ( x i +1 ) = S 00 i +1 ( x i +1 ) for i = 0 , 1 , 2 ,...,n 2 S 00 ( x ) = S 00 n 1 ( x n ) [ free boundary condition ] or S ( x ) = f ( x ) and S n 1 ( x n ) = f ( x n ) [ clamped boundary condition...
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This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.
 Summer '08
 Kyung
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