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quadratic convergence (Definition)

A sequence $ \{x_i\}$ in a metric space $ (X,d)$ is said to converge quadratically to $ x^*$ if there is a constant $ 1>c>0$ such that $ d(x_{i+1},x^*) \leq c d(x_i,x^*)^2$ for all $ i$.

The convergence is said to be of order $ p$ if $ d(x_{i+1},x^*) \leq c d(x_i,x^*)^p$ for all $ i$.



"quadratic convergence" is owned by Koro. [ full author list (2) | owner history (1) ]
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See Also: linear convergence
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Cross-references: order, converge, metric space, sequence
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This is version 5 of quadratic convergence, born on 2004-05-02, modified 2004-06-16.
Object id is 5825, canonical name is QuadraticConvergence.
Accessed 3767 times total.

Classification:
AMS MSC: 41A25 (Approximations and expansions :: Rate of convergence, degree of approximation)
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