8. (15 pts) The Hilbert matrix Hn (hiji-1 of order n is defined by This matrix i

Question

8. (15 pts) The Hilbert matrix Hn (hiji-1 of order n is defined by This matrix is nonsingular and has an explicit inverse. However, as n increases, the condi- tion number of Hn increases rapidly. The MATLAB functions hilb(n) and invhilb(n) give Hn and H respectively. Let x (1,1,, 1) and b Hnx. This problem examines the two fundamental principles regarding the quality of the computed solution x* (a) Forn 5, 10, set x using the command ones, multiply H,x, to obtain b, and then solve for x with the MATLAB backslash command. (b) Compute the error e xn x, the residual rn bn Hnx, and their norms o with the command norm. Draw conclusions

Explanation / Answer

H = hilb(5) ; (used to define hilbert matrix of order n)

X = [1, 1, 1, 1, 1] ; (to define matrix X)

b = HX ;

X = H; ( Backslash command is used to solve b = HX)

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