I have attempted 2 question instead of 1 . solution being lengthy all three answers cant be reasonable
if you need any further clarification regarding first two question feel free to comment below
Homework Problem Set 16 x-1)3 for 0 sx$1 a cubic spline? 1. Is the function s (x) = {2(-1)3 for 1...
2. Consider the cubic spline for a function f on [0, 2] defined by S(x) = { ={ (z. 2x3 + ax2 + rx +1 if 0 < x <1 (x - 1)3 + c(x - 1)2 + d(x - 1) + ß if 1 < x < 2 where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Define the following functions, and verify if cubic splie on given interval, also determine if natural spline. on al Define: Sx) = -5+86-66x² + 2x3 12XL 2 land S(x) = 27-40x +18% - 2x² on. 22X<3 b) Verify that Sx) is a cubic spline function on 6 Is it a natural spline function on this interual?
Problem 3: Write a MATLAB function called cubic_spline to compute the natural cubic spline for a given data set. The x and y data points and the rdesired values (a vector) should be the inputs, and the corresponding ydesired values (a vector) should be the output.
Alpha=9 beta=3 yazarsin 2. ( 20p.) Consider the cubic spline for a function f on (0,2) defined by 2x3 + x² +rx +1 if 0 <x<1 S(x) = (x - 1)3 + c(x - 1)2 + d(x - 1) + B if 1<x<2 = {(2-1) where r,c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
s(x)=x3+x2+x+1 for 0≤x≤1, s(x)=-x3+7x2-5x+3 for 1<x≤2. Is the function a cubic spline?
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
2. A natural cubic spline S is defined by S(z) = { $(") = 11 S. (C)=1+ B(-1) + D(x - 1)3 S (2)=1+b(-2) + 3(x - 2)2 + (x - 2) if 1 <3 <2 if 2 <3<3 Find B, D, b, and d. Hint: Recall that a natural cubic spline has S" equal to 0 at the endpoints.
0.19 0.. 1. (Natural Splines) Find the natural cubic spline S(x) satisfying S(0) = 0, S(1/2) = 1, S(1) = 0. Your answer will be 2 cubic polynomials, S.(x), S1(x). Verify that your answer satisfies all the necessary conditions (interpolation, continuity of 1st and 2nd derivatives, boundary conditions). We were unable to transcribe this image
2. More on Cubic Splines Consider the data Xi : 1 2 3 4 Yi : 18 27 64 a. Construct the cubic interpolant, i.e., find the cubic polynomial p that satisfies p(xi) = Yi, i = 1,2,3,4 and draw its graph. b. Construct the interpolating natural cubic spline and draw its graph. c. Comment on your results.
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?