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?
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?
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.
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.
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.
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
5. Use Scilab to create following rational expression matrix: 12x 2 1+x 1x2 1 x2 1 +x 3 x 1+x3x3 5x x3 2 x2 1 x3 6 1+2x 1+ 3х + x2 1-х+x2.
5. Use Scilab to create following rational expression matrix: 12x 2 1+x 1x2 1 x2 1 +x 3 x 1+x3x3 5x x3 2 x2 1 x3 6 1+2x 1+ 3х + x2 1-х+x2.
Evaluate the following integrals.
S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
Numerical analysis
Question 1 A clamped cubic spline Six) on interval [0, 2) is defined by S(x) - 3 + ax + bx2 - 2x06x<1 (3 + c(x - 1) - 4(x - 1)2 + 7(x - 1) 1sx52 where a, b, care constants. Find the values of S'(0) and S(2).
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?