Local convergence

In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. Iterative methods for nonlinear equations and their systems, such as Newton's method are usually only locally convergent.^[1]

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.^[1]

References

^ ^a ^b Gautschi, Walter (2012). Numerical analysis (2nd ed.). New York: Springer / Birkhäuser. p. 275. ISBN 978-0-8176-8258-3.

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[:0-1] Gautschi, Walter (2012). Numerical analysis (2nd ed.). New York: Springer / Birkhäuser. p. 275. ISBN 978-0-8176-8258-3.

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