Determine by hand calculation (show all steps) the clamped cubic spline that interpolates the data f(-3)...

Determine by hand calculation (show all steps) the clamped cubic spline that interpolates the data f(-3) = 2 ; f(-1) = -3 ; f(0) = 1 ; f(3) = 6 ; f(5) = 3 and satisfies s'(-3) = s'(5) = 0

Expert Solution

Colby Messinger answered 2 years ago

The question is to use Matlab to find the clamped cubic spline v(x) that interpolates a...

The question is to use Matlab to find the clamped cubic spline v(x) that interpolates a function f(x) that satisfies: f(0)=0, f(1)=0.5, f(2)=2, f(3)=1.5, f'(0)=0.2, f'(3)=-1 and then plot v(x). This is my code so far: x = [0 1 2 3]; y = [0 0.5 2 1.5]; cs = spline(x,[0 y 0]); xx = linspace(0,3,101); figure() plot(x,y,'o',xx,ppval(cs,xx),'-'); IS THIS RIGHT? HOW CAN I GET MATLAB TO GIVE ME THE EQUATION OF v(x)?

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S(x) is a cubic spline for the function f(x) = sin(pi x/2) + cos(pi x/2) at the nodes x0 = 0 , x1 = 1 , x2 = 2 and satisfies the clamped boundary conditions. Determine the coefficient of x3 in S(x) on [0,1] ans. pi/2 -3/2

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a) For the function f (x) = x – exp(−x2), do a calculation by hand using...

a) For the function f (x) = x – exp(−x2), do a calculation by hand using a calculator to find the root to an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy. b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of Newton’s method (by hand); tabulate the result.

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Show all calculation details by not using a calculator or Excel answers. Consider the data set:...

Show all calculation details by not using a calculator or Excel answers. Consider the data set: (7,11), (10,0), (13,-2). A. Compute and interpret the coefficient of correlation. B. Compute the least squares line for this data (no need to repeat computations from above).

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