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Thread View: sci.math.num-analysis
1 messages
1 total messages Started by roberto bagnara Thu, 16 Apr 1992 08:53
Numerical analysis newsletters?
#300
Author: roberto bagnara
Date: Thu, 16 Apr 1992 08:53
29 lines
1578 bytes
Hi all,

    while studying for an elementary course in numerical analysis
I've found a nice unified proof for the convergence of both the
Jacobi and Gauss-Seidel methods for solving systems of linear equations
under the following conditions:

    a) strict diagonal predominance (by rows or by columns);
    b) non-strict diagonal predominance (by rows or by columns)
       and irreducibility.

    These results are obviously known to everybody, but the proof
I've found is very simple and (I believe) elegant. At least it is
much more simple and elegant than the disaggregated proofs I've
found in my textbook and a couple of others I've consulted (it
is *one* proof, and it is based on spectral considerations rather
than on low-level details).
I don't know if the proof is original and, even if it is, I think
that it's main importance could be for teaching purposes. A couple
of mathematicians, friends of mine, agree on that.

    The question is the following: is there any numerical analysis
journal/newsletter publishing also short-notes/letters that
(after checking for originality) could publish this proof?
If so would send me their address?

Please respond by EMail. Thanks in advance
                                            Roberto
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