“rate of convergence”的概念、定义、翻译、参考文献-科学参考

rate of convergence

Mathematics

单词	rate of convergence
释义	rate of convergence Mathematics A sequence {x_n} which converges to a limit l is said to have rate (or order) of convergence r ≤ 1 if there exists M such that $\| x_{n + 1} - l \| \leq M {\| x_{n} - l \|}^{r}$ for sufficiently large n. For r = 1, it is further required that M ≤ 1. If r = 2, then the convergence is said to be quadratic. If r = 1 and ${lim}_{n \to \infty} \frac{\| x_{n + 1} - l \|}{\| x_{n} - l \|} = m,$ then the convergence is said to be superlinear, linear, or sublinear depending on whether m = 0, 0 < m < 1 or m = 1.
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