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Topic: Re: [mg5340] Re: [mg5303] Euclidean Matrix Norm
Replies: 0

 Allan Hayes Posts: 1,508 Registered: 12/6/04
Re: [mg5340] Re: [mg5303] Euclidean Matrix Norm
Posted: Dec 1, 1996 11:24 PM

Lou Talman <me@talmanl.mscd.edu>
Subject: [mg5340] Re: [mg5303] Euclidean Matrix Norm

>The matrix norm of the square matrix A is the square root of the
>largest eigenvalue of the matrix (Transpose[A] . A), so put
>
> Norm[A_] := Sqrt[Max[N[Eigenvalues[Transpose[A].A]]]]

Lou,
Better move the N inside:

A = Table[Random[Integer,{-9,9}],{4},{4}]
{{-9, -9, 9, -1}, {-7, -6, -4, 1}, {-3, 0, 1, -4}, {3, 2, -5, 2}}

Sqrt[Max[N[Eigenvalues[Transpose[A].A]]]]//Timing
-15
List::nord: Comparison with complex number 0.0174327 - 2.55892 10 I
attempted.
-15
{1.35 Second, Sqrt[Max[{0.0174327 - 2.55892 10 I,
-15 -16
19.8739 + 3.16651 10 I, 77.0539 - 6.37398 10 I,
-17
317.055 + 2.98003 10 I}]]}

Chop[%]

{1.35 Second, 17.806}

But with N inside

Sqrt[Max[Eigenvalues[Transpose[A//N].A//N]]]//Timing

{0. Second, 17.806}

Allan Hayes
hay@haystack.demon.co.uk
http://wwe.haystack.demon.co.uk