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Gauss–Seidel method
In
numerical linear algebra
, the
Gauss–Seidel method
, also known as the
Liebmann method
or the
method of successive displacement
, is an
iterative method
used to solve a
linear system of equations
. It is named after the
German
mathematicians
Carl Friedrich Gauss
and
Philipp Ludwig von Seidel
, and is similar to the
Jacobi method
. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either
diagonally dominant
, or
symmetric
and
positive definite
. It was only mentioned in a private letter from Gauss to his student
Gerling
in 1823. A publication was not delivered before 1874 by Seidel.
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