Numerical Linear Algebra with Applications

NLALIB: The function hhess implements Algorithm 18.2.

Example 18.9

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 ...