Calculating norm of a function

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3 total messages Started by John J. Sasso Jr. Mon, 04 Jan 1993 18:10

#1001

Author: John J. Sasso Jr.
Date: Mon, 04 Jan 1993 18:10

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   Given a function f in L^2(R), which exists on the interval [a,b], how
would I go about calculating its L^2-norm?  Does there exist a numerical
algorithm which can do this?

                         -- John

Re: Calculating norm of a function

#1005

Author: Sadasivan Shankar
Date: Mon, 04 Jan 1993 20:09

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Your problem looks like that of finding a Cauchy sequence in the L2 norm.  Typically, this
seems to be a Hilbert-space problem, where a converging series is used to find the
norm of a function. Does anybody else have a comment on this ?

S.Shankar
Tech CAD
INTEL Corporation

Re: Calculating norm of a function

#1026

Author: Richard Simard
Date: Tue, 05 Jan 1993 18:58

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In article <!672sl_@rpi.edu> sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:
>
>   Given a function f in L^2(R), which exists on the interval [a,b], how
>would I go about calculating its L^2-norm?  Does there exist a numerical
>algorithm which can do this?
>
the simplest choice of norm would be:

integral(from a to b) dx f*(x) f(x)
where f* is the complex conjugate

- if f is real then 
integral(from a to b) dx f(x)^2

other choices of norms are possible depending on your problem;
for ex.

integral(from a to b) dx f(x)^2/[(x-a)(b-x)]^t

where t is a real such that the integral exists.

--
From:  simardr@iro.umontreal.ca

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