3.4 (Graded) Cubic splines 2. Determine the clamped cubic spline s that interpolates the data f (0) 0, f(1) 1, f(2) 2 and satisfies s' (0) = s'(2) = 1 Note: this can be done effectively by hand. 4c....

#16 from this handout

From Numerical Analysis 8th Edition by Richard Burden, Section 3.4

Extracted text: 3.4 (Graded) Cubic splines 2. Determine the clamped cubic spline s that interpolates the data f (0) 0, f(1) 1, f(2) 2 and satisfies s' (0) = s'(2) = 1 Note: this can be done effectively by hand. 4c. Construct the natural cubic spline for the following data. f (x) х -0.29004996 0.1 -0.56079734 0.2 -0.81401972 0.3 Note: this can be done effectively with the aid of software - avoid ugly numbers by hand. 8c. Construct the clamped cubic spline using the data of Exercise 4 and the fact that f'(0.1) =-2.801998 and f'(0.3) = -2.453395. Note: Book has f(0.1) listed incorrectly. Also this can be done effectively with the aid of software avoid ugly numbers by hand. 12. A clamped cubic splines for a function f is defined on [1,3] by Jso()3(-1)+2( -1)2 - (x - 1)3, if 1 < 2 s1()a+b(x - 2)+ c( - 2)2 + d(x - 2)3, s(x) = if 2 2="" s1()a+b(x="" -="" 2)+="" c(="" -="" 2)2="" +="" d(x="" -="" 2)3,="" s(x)="if">