The n x n Hilbert matrix (see page 519) defined by HP = I 7-1' I < A 7 < n, is an
Chapter 7, Problem 9(choose chapter or problem)
The n x n Hilbert matrix (see page 519) defined by HP = I 7-1' I < A 7 < n, is an ill-conditioned matrix that arises in solving the normal equations for the coefficients ofthe least squares polynomial (See Example 1 of Section 8.2). a. Show that l//'41]-' = 16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800 b. and compute Show that l//]"1 = c. and compute Solve the linear system 25 -300 1050 -1400 630 -300 4800 -18900 26880 -12600 1050 -18900 79380 -117600 56700 -1400 26880 -117600 179200 -88200 630 -12600 56700 -88200 44100 H (4) X\ 1 X2 0 *3 0 . X 4 1 using five-digit rounding arithmetic and compare the actual error to that estimated in (7.25)
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