The n n Hilbert matrix H is defined by h(i, j ) = 1/(i + j 1) i, j = 1, 2, . . . , n It
Chapter 7, Problem 4(choose chapter or problem)
The n n Hilbert matrix H is defined by h(i, j ) = 1/(i + j 1) i, j = 1, 2, . . . , n It can be generated with the MATLAB function hilb. The Hilbert matrix is notoriously ill conditioned. It is often used in examples to illustrate the dangers of matrix computations. TheMATLAB function invhilb gives the exact inverse of the Hilbert matrix. For the cases n = 6, 8, 10, 12, construct H and b so that Hx = b is a Hilbert system whose solution in exact arithmetic should be ones(n, 1). In each case, determine the solution x of the system by using invhilb and examine x with format long. How many digits of accuracy were lost in each case? Compute the condition number of each Hilbert matrix. How does the condition number change as n increases?
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