The 3 3 Hilbert matrix is The n n Hilbert matrix is H n h jk , where h jk 1 (j k 1) (Similar matrices occur in curve fitting by least squares ) Compute the condition number (H n ) for the matrix norm corresponding to the l (or l 1 ) vector norm, for n 2, 3, , 6 (or further if you wish) Try to find a formula that gives reasonable approximate values of these rapidly growing numbers Solve a few linear systems of your choice, involving an H n

Question: The 3 3 Hilbert matrix is The n n Hilbert matrix is H n = [h jk ], where h jk = 1/(j

The 3 × 3 Hilbert matrix is

The 3 × 3 Hilbert matrix is The n × n Hilbert

The n × n Hilbert matrix is H_n = [h_jk], where h_jk= 1/(j + k - 1). (Similar matrices occur in curve fitting by least squares.) Compute the condition number κ(H_n) for the matrix norm corresponding to the l_∞ - (or l₁-) vector norm, for n = 2, 3, · · ·, 6 (or further if you wish). Try to find a formula that gives reasonable approximate values of these rapidly growing numbers.

Solve a few linear systems of your choice, involving an H_n.

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