Problem 17 Find the natural cubic spline through (0,3), (1,2), and (2,1). Show transcribed image text
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...
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
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.
Find the periodie cubie spline sp(x) passing through the 3 points (^j, yj) given by (0, 1), (2,1), and (3,2). Then evaluate sp(1)
Find the periodie cubie spline sp(x) passing through the 3 points (^j, yj) given by (0, 1), (2,1), and (3,2). Then evaluate sp(1)
T47:02 731 VPN 97% 5 TOⓇ + : 6. Find the natural cubic spline to approximate f(0) = 32 – 1 at 3o = 0,01 = 0.25, 12 = 0.5, 23 = 0.75 and 24 = 1. 13
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?
Determine the reactions at the supports. El is a constant Prob. 15-7 12 kN/m 2.5 m Show transcribed image text Solve using the stiffness method
(C) For the function g:R → Z by g(2) = find 9-1({-1,2}).
SHOW ALL WORK THROUGH MINITAB ONLY! Thank you! a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates (1,2), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b). 104TILL JOINT ott 0 2 4 6 8 10 Answer the following questions: 1. What is the equation of the...
2. A line passes through the points A(-2,1) and B(1,7), find its equation. please show work