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NLALIB: The function hhess implements Algorithm 18.2.
Let A be the matrix of Example 18.8. The MATLAB commands use hhess to transform A to upper Hessenberg form and then verify that PAPT = H within expected roundoff error.
>> [P H] = hhess(A);
>> norm(P*H*P’ - A)
Algorithm 18.2 requires 103n3 flops for the computation of H. To build ...