
A Unified Proof for the Convergence of Jacobi and GaussSeidel Methods
Roberto Bagnara
Abstract:We present a new unified proof for the convergence of both the Jacobi and the GaussSeidel methods for solving systems of linear equations under the criterion of either (a) strict diagonal dominance of the matrix, or (b) diagonal dominance and irreducibility of the matrix. These results are well known. The proof for criterion (a) makes use of Gersgorin's theorem, while the proof for criterion (b) uses Taussky's theorem that extends Gersgorin's work. Hence the topic is interesting for teaching purposes.
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bagnara@cs.unipr.it 
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