Infinite system of linear equations - sci.math

Message from discussion Infinite system of linear equations
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From: "Klueless" <kluel...@worldnet.att.net>
Newsgroups: sci.math
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Subject: Re: Infinite system of linear equations
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Date: Mon, 13 Nov 2006 16:42:20 GMT
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"Jules" <julianro...@gmail.com> wrote in message news:1163398359.617744.163980@k70g2000cwa.googlegroups.com...
> We wish to find a sequence {a_j} of reals so that the
> sum as j goes from 1 to infinity of b_(i, j) * a_j = c_i for each i.
> This is, in some sense, a collection of countably-many linear equations
> in countably-many variables.

     This is a discrete form of an integral equation.  Viewing
a(j), b(i,j), c(i) as step functions in i, j, you see you are solving

     Int(b(i,j)*a(j),j=0..infinity) = c(i)

for the unknown function a(j).

<http://en.wikipedia.org/wiki/Integral_equation>
<http://mathworld.wolfram.com/IntegralEquation.html>
<http://mathworld.wolfram.com/FredholmIntegralEquationoftheFirstKind.html>