10-16 DETERMINATION OF SPLINES Find the cubic spline g(x) for the given data with ko and...
1. Fit cubic splines to the following data
(1) using natural end condition and estimate f(4.0) with the
cubic spline.
(2) using clamped end condition with f1’=-2.5, f5’=3.0 and
estimate f(4.0) with the cubic spline.
(3) using “not-a-knot” end condition and estimate f(4.0) with
the cubic spline.
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
4 2 9.0 7.0 5.0 2.5 1.0 Xi 2.5 0.5 2.5 1.0 fi 2,5 er
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
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline.
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) 2+y=9, 22 + y2 = 25, 2,y> 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as the initial solution. [20]
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, F (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
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...
2.3.7 Given that f(x) 3x + 4 and g(x)x°, find (f o g)(-2). (fo g)-2)
in MATLAB Curve fitting Given the following data, find the best linear functional relationship and cubic functional relationship using “polyfit,” “polyval,” and “plot” built-in functions. Plot all three fits that you got from Matlab. A rough plot by hand is allowable. You do not need to provide any codes. x = [-3, -2, 0, 1, 3, 4, 6, 7, 8, 9]; y = [5, 7, 8, 10, 6, 2, -4, -6, -2, 1];
5. [2p] (a) In a two-dimensional linear space X we are given three bases e-(a, e f- (fi, f2), and g- (91,92). The change of basis matrix from the basis f to the basis e 3 and the change of basis matrix from the basis g to the basis f is ) 3 2) Finod the change of basis matrix from the basis g to the basis e 4 -5 15 12 12 -2 -8 2(B) 16 1)(E) 05 9...
Question 14 Given f(x) = – 2x – 1 and g(x) = V2 – 9, find f (g-1(x)) = Submit Question x Question 15 Score on last try: 0 of 5 pts. See Details for more. Try a similar question You can retry this question below Let f(x) = 4 + vx – 4. Find f-1(x). f-1(x) = Now for fun, verify that (fo f-1)(x) = (f-10 f)(x) = = 2 Submit Question