Determine the value of the coefficients a, b, c, d and e so that the following...
14. Let so(z) = 1+c(x+1)3 for-1 < z < 0 for some real constant c. Determine s1() for 0 S 1 such that so(x) s1() for 0S for-1 < x < 0; s(x) = 1 is a natural cubic spline on [-1, 1] with nodes at 1,0,1. How must c be chosen if one wants s(1) =-1?
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.
5. (10 points) Determine the coefficients in the function such that it is a cubic spline that takes the value 1 when x = 2.
(x0,y0), (x1,y1) Using natural cubic spline, how can I get
ax^3+bx^2+cx+d formula? (can a, b, c, d=0)
Describe explicitly the natural cubic spline that interpolates a table with only two entries: 0 Give a formula for it. Here, to and t are the knots.
Describe explicitly the natural cubic spline that interpolates a table with only two entries: 0 Give a formula for it. Here, to and t are the knots.
Find the natural cubic spline interpolant to f(x) = e^(x^3) at the nodes {xi} i=0 = {−2, 0, 2} . Calculate the value of the interpolant at x = 1. What is the error at this point?
[T2] This problem concerns the derivation of the equations used to determine the coefficients of a quadratic spline approximation, S(x), to a function F(x) over an interval [x min, Xmax]. To assist in getting the indices correct, it is suggested you draw a picture that displays the labeling of the values involved. In the computational part of this assignment, you will be setting up and solving these equations. • Assume that n panels are used and the knots {x;} are...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
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?
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.
I need help with parts A B D E and F. Please show hand work
for solving A and B while D and E should be matlab codes. How do i
pick the right graph for part F?
5 2 4 6 Linear spline: s fi+ (x-x) 2) Given the points 40 78 125 256 348 425 X1-x a) Write the correct linear spline equation to interpolate for x 4.72, simplifying where appropriate to get to the slope-intercept form. (4...