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Numerical Linear Algebra with Applications by William Ford

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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 PAPT = H within expected roundoff error.

 >> [P H] = hhess(A);
 >> H
 H =
9-5.1832-0.014905-1.9323-0.63263
-11.57618.76111.6590.5625-3.7232
07.69880.015962.3683-3.1455
000.57652-0.613112.5435
000-0.461416.836

t0020

 >> norm(P*H*P’ - A)
 ans =
  2.1495e-014

18.4.1 Efficiency and Stability

Algorithm 18.2 requires 103n3si180_e flops for the computation of H. To build ...

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