define linear convergence and quadratic convergence
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Answer:
Step-by-step explanation:One of the ways in which algorithms will be compared is via their rates of convergence to some limiting value. Typically, we have an interative algorithm that is trying to find the maximum/minimum of a function and we want an estimate of how long it will take to reach that optimal value. There are three rates of convergence that we will focus on here—linear, superlinear, and quadratic—which are ordered from slowest to fastest.
In our context, rates of convergence are typically determined by how much information about the target function
f
we use in the updating process of the algorithm. Algorithms that use little information about
f
, such as the bisection algorithm, converge slowly. Algorithms that require more information about
f
, such as derivative information, typically converge more quickly. There is no free lunch!