In
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...
, an
iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived from the pr ...
is called locally convergent if the successive
approximations produced by the method are guaranteed to
converge
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*CONVERGE CFD s ...
to a solution when the initial approximation is already close enough to the solution. Iterative methods for
nonlinear equation
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
s and their systems, such as
Newton's method are usually only locally convergent.
An iterative method that converges for an arbitrary initial approximation is called globally convergent. Iterative methods for systems of
linear equations are usually globally convergent.
Numerical analysis
Iterative methods
Optimization algorithms and methods
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