5. (10 points) Determine the coefficients in the function such that it is 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.
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 < x 2 -5 +8x-6x2 2x3 for1 sx s 2 Is the function s(x)-[ natural? Let x for j 1,2,3,4 by a calculation on paper 3 a cubic spline? Is it [1,0,1,0]. Determine the natural spline s with s(y)-yi 2. 18x2-2x3 for 2
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.
3D Cubic B-Spline Interpolation and Error Estimation Theme: Implement and study 3D Cubic Spline Interpolation Input: a set of points in 3D space (data(x,y,z)) Output: Spline, Spline data points and error, 3D graph that shows the original points and the Spline The major steps involved in the B-Spline Fitting and Error Estimation are as mentioned below: 1- Sample the data points from input data. 2- Interpolate to find the position of control points. 3- Use the B-Spline basis function to...
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?
Q4 Spline 5 Points A spline function is a smooth interpolation. O True O False Q5 Polynomial 5 Points For-1 < x < 1 the expression cos(n arccos x) is a polynomial of degree n. True False
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with uniform point spacing h=5m-x, for jso,1,..,,n. Ifthe symbols M,, 0, represent the second derivatives of the spline at cach of the mesh points, show that in each intervl-.R-1 For the natural cubic spline (for which M, O and M-=0 ), show that the moments M...
Write a complete set of Matlab instructions that implements cubic spline interpolation on the following data (assume clamped-end-condition). Your code should: a. Generate a single plot, over the range 0<= x <= 5, displaying: i. the individual data points ii. the generated spline function b. Predict the interpolated value at x = 0.5, x = 0.8 and x = 3.7 X у 0 1.7 1 0.3 2 1.8 3 0.4 4 2
Design a MATLAB code to construct a natural cubic spline P(x) that passes though the points (1, 1), (4, 1/4), (7, 1/7), (10, 1/10), (13, 1/13) and (16, 1/16). (a) Use the constructed cubic spline to interpolate x = 3; (b) Find the error e_1 = |1/3 - P(3)|;
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.