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 Post subject: Gauss SeidelPosted: Thu, 30 Sep 2010 06:02:42 UTC
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Hi, I'm trying to do the matrix method for Gauss Seidel and the iterations are coming out different than the equation method so i wanted to know if anyone could explain to me how to go about doing the gauss seidel method with matrices i have

so I created the strictly upper matrix and the lower matrix and got

Lower:

Strictly Upper

then I found the inverse of the Lower matrix

then i found Linverse*U and Linverse*b

then used the iterative method of

and for my first iteration i got

with an initial guess of

and the solution vector is

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 Post subject: Re: Gauss SeidelPosted: Thu, 30 Sep 2010 07:06:24 UTC
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David the Mathlete wrote:
Hi, I'm trying to do the matrix method for Gauss Seidel and the iterations are coming out different than the equation method so i wanted to know if anyone could explain to me how to go about doing the gauss seidel method with matrices i have

so I created the strictly upper matrix and the lower matrix and got

Lower:

Strictly Upper

then I found the inverse of the Lower matrix

then i found Linverse*U and Linverse*b

then used the iterative method of

and for my first iteration i got

with an initial guess of

and the solution vector is

Gauss-Seidel is an iterative method, and there are no reason to expect you arrive at the exact solution with just one iteraton.

In your example, the matrices are

and the iterative scheme is

i.e.

So the iterative scheme yields

Compare this with the exact solution

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