Gauss–Seidel method

<p>In <a href="/facts/Numerical_linear_algebra/jnS6Tteb">numerical linear algebra</a>, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement,  is an <a href="/facts/Iterative_method/uKMAJhEh">iterative method</a> used to solve a <a href="/facts/System_of_linear_equations/fk9CFdgp">system of linear equations</a>. It is named after the <a href="/facts/Germany/paluuWBX">German</a> <a href="/facts/Mathematician/eaFSR8Fx">mathematicians</a> <a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a> and <a href="/facts/Philipp_Ludwig_von_Seidel/slnmo9Qn">Philipp Ludwig von Seidel</a>. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either <a href="/facts/Diagonally_dominant_matrix/qbRQV7CV">strictly diagonally dominant</a>, or <a href="/facts/Symmetric_matrix/08CGwjNl">symmetric</a> and <a href="/facts/Positive-definite_matrix/Hbr6AuPS">positive definite</a>. It was only mentioned in a private letter from Gauss to his student <a href="/facts/Christian_Ludwig_Gerling/fvQbCs8f">Gerling</a> in 1823. A publication was not delivered before 1874 by Seidel.
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Gauss–Seidel method open-in-new

Gauss–Seidel method