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 PAP^{T} = H within expected roundoff error.

>> [P H] = hhess(A);
>> H
H =

9

-5.1832

-0.014905

-1.9323

-0.63263

-11.576

18.761

11.659

0.5625

-3.7232

0

7.6988

0.01596

2.3683

-3.1455

0

0

0.57652

-0.61311

2.5435

0

0

0

-0.46141

6.836

>> norm(P*H*P’ - A)
ans =
2.1495e-014

18.4.1 Efficiency and Stability

Algorithm 18.2 requires $\frac{10}{3}{n}^{3}$ flops for the computation of H. To build ...

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