Given f(x)=sin(x)-x3+1, explicitly write down the error term, E, (x), for the cubic Lagrange interpolating polynomial...

  

Transcribed Image Text:

Given f(x)=sin(x)-x3+1, explicitly write down the error term, E, (x), for the cubic Lagrange interpolating polynomial of f(x) with x = -0.6, x = 0.3, x2 = 0.6, x3 = 2.2 and estimate the error at x=1.78 using the Lagrange error formula. a. Explicitly write out the error formula, E,,(x) b. Estimated error at x=1.78, E (1.78)= c. Plot the error function in MATLAB, that is, the 3 dimensional plot as demonstrated in the problem videos using meshgrid to set up the (x,y) variables for evaluation of the error formula and the mesh plot command to plot the function. Recall that the theoretical error function is actually a function of 2 variables as indicated in the notes and videos. Given f(x)=sin(x)-x3+1, explicitly write down the error term, E, (x), for the cubic Lagrange interpolating polynomial of f(x) with x = -0.6, x = 0.3, x2 = 0.6, x3 = 2.2 and estimate the error at x=1.78 using the Lagrange error formula. a. Explicitly write out the error formula, E,,(x) b. Estimated error at x=1.78, E (1.78)= c. Plot the error function in MATLAB, that is, the 3 dimensional plot as demonstrated in the problem videos using meshgrid to set up the (x,y) variables for evaluation of the error formula and the mesh plot command to plot the function. Recall that the theoretical error function is actually a function of 2 variables as indicated in the notes and videos.