Examples include Newton's method, the bisection method, and Jacobi iteration.
2.
Dekker's method requires far more iterations than the bisection method in this case.
3.
A few steps of the bisection method applied over the starting range [ a 1; b 1 ].
4.
The secant method does not require that the root remain bracketed like the bisection method does, and hence it does not always converge.
5.
The "'bisection method "'in mathematics is a root-finding method that repeatedly root must lie for further processing.
6.
Division by zero can lead to separation of distinct zeros, though the separation may not be complete; it can be complemented by the bisection method.
7.
Analogously with the bisection method, the algorithm is then applied recursively to any quarter whose boundary has nonzero winding number to further refine the estimates of the zeros.
8.
Brent proved that his method requires at most " N " 2 iterations, where " N " denotes the number of iterations for the bisection method.
9.
:If " x " = log 10 2 then 10 " x " & minus; 2 = 0 and we can solve the latter using a root-finding algorithm such as the bisection method or Newton's method.
10.
If the situation were a little trickier, and the solution not a simple integer ( eg . if you were trying to solve 2 ^ x + x = pi ), then your best bet is to find an approximate solution using, for example, the bisection method or Newton's method.
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