Consider the linear system Ax = b with
and b such that the corresponding solution is x = (1, 1, 1)T
and _ is a positive real number. Compute the LU factorization of A
and note that l32 when _ _ 0. Verify
that the computed solution is not affected by rounding errors when _
= 10_k with k = 0, .., 9 and b = (0, _,
2)T . Moreover, analyze the relative error on the exact solution
when _ = 1/3 · 10_k with k = 0, .., 9, and
the exact solution is xex = (log(5/2), 1, 1)T .
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