In Equation (10-7), show that if N 6 n then the solution of is non-unique. For

In Equation (10-7), show that if N 6 n then the solution of β is non-unique. For the example in Problem 10.2-3, calculate the error bound when the polynomial order n is exactly equal to the number of samples N = 10.

Equation 10-7

Problem 10.2-3

Consider the sinusoidal function y(k) = sin (10 k) for k = 0, 1, . . . , 9. Find the minimum degree of the polynomial which fits this function with a maximum least-squares error of 10^-3.

Transcribed Image Text:

y(0) y(1) y(2) = 1 1 1 u(0) u(0) u(1) u(2) u(1) u(2) u(N) u(N) *** ... ... u" (0) u" (1) u" (2) u" (N) Bo B B B (10-7)