Roberto, Margherita and Beatrice


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A Unified Proof for the Convergence of Jacobi and Gauss-Seidel Methods

Roberto Bagnara
Dipartimento di Informatica
Università di Pisa
Corso Italia 40
I-56125 Pisa


We present a new unified proof for the convergence of both the Jacobi and the Gauss-Seidel 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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[Page last updated on December 10, 1999, 11:30:49.]

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