![]() What makes the Jacobi and Gauss-Seidel methods work These. This article incorporates text from the article Gauss-Seidel_method on CFD-Wiki that is under the GFDL license. Keep in mind that our first example might involve 10,000 linear equations in 10,000 variables. (1996), Matrix Computations (3rd ed.), Baltimore: Johns Hopkins, ISBN 978-0-8018-5414-9. With the Jacobi method, the values of obtained in the th iteration remain unchanged until the entire. Gauss, Carl Friedrich (1903), Werke (in German), vol. 9, Göttingen: Köninglichen Gesellschaft der Wissenschaften."A Unified Proof for the Convergence of Jacobi and Gauss-Seidel Methods". Abhandlungen der Mathematisch-Physikalischen Klasse der Königlich Bayerischen Akademie der Wissenschaften (in German). The only difference is that we exchanged first and the third equation with each other and that made the coefficient matrix not diagonally dominant. ![]() However, it is the same set of equations as the previous example and that converged. "Über ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineäre Gleichungen überhaupt, durch successive Annäherung aufzulösen". Hence, the Gauss-Seidel method may or may not converge.
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