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(Solved): EE202 Numerical Methods for Engineers Laboratory Assignment: 4 Given Problem ...
EE202 Numerical Methods for Engineers Laboratory Assignment: 4 Given Problem 1: Write the a MATLAB program to compute the cardinal polynomials (i.e. its coefficients) appropriate to the problem of interpolating the above table. Problem 2: Plot the cardinals polynomials in the same figure. Problem 3: In the same MATLAB program compute Lagrange form of the interpolating polynomial (i.e. its coefficients). Problem 4: Plot the Lagrange form of the interpolating polynomial in another figure. On the same figure, plot the data points given in the above table.
Expert Answer
Problem 1: To compute the cardinal polynomials, we can use the following MATLAB code:This code first defines the input data, with n being the number of data points, xn being the x-coordinates of the data points, and yn being the y-coordinates of the data points.It then uses two nested loops to compute the cardinal polynomial for each data point. For each data point i, the inner loop multiplies together the terms (x - xn(j)) / (xn(i) - xn(j)) for all other data points j except for i. This gives the polynomial p(x) corresponding to the cardinal function l_i(x). The polynomial coefficients are stored in the matrix c, with each column corresponding to a different data point.Note that we use the conv function to multiply polynomials together. The resulting polynomial has length 2n - 1, where n is the degree of the polynomial. We also normalize the coefficients by dividing by the leading coefficient, so that the leading coefficient is always 1.