Newton's Method: Convergence and Quadratic Convergence

Description

This lecture continues the exploration of Newton's method, focusing on the convergence properties and quadratic convergence. The theorem 8.4 is presented, showing the conditions for convergence and the speed of convergence. The lecture also discusses situations where Newton's method may fail to converge, providing insights into the behavior of the method in different scenarios.

In MOOCs (4)

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Related concepts (34)

Rate of convergence

In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence that converges to is said to have order of convergence and rate of convergence if The rate of convergence is also called the asymptotic error constant. Note that this terminology is not standardized and some authors will use rate where this article uses order (e.g., ).

Uniform convergence

In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .

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Applied behavior analysis

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