Why the bisection method is slower than Newton's method from a complexity point of view?

lunja55
2022-09-27
Answered

Why the bisection method is slower than Newton's method from a complexity point of view?

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Davian Nguyen

Answered 2022-09-28
Author has **9** answers

Why the bisection method is slower than Newton's method from a complexity point of view?

asked 2022-10-12

Estimate the number of iterations of Newton's method needed to find a root of $f(x)=\mathrm{cos}(x)-x$ to within ${10}^{-100}$.

asked 2022-11-08

Prove that Newton's Method applied to $f(x)=ax+b$ converges in one step? Would it be because the derivative of $f(x)$ is simply $a$?

asked 2022-07-19

Use Newton's method to find the roots of

$2{x}^{3}-9{x}^{2}+12x+15$

for $x=3$, $x<-3$, and $x>3$.

$2{x}^{3}-9{x}^{2}+12x+15$

for $x=3$, $x<-3$, and $x>3$.

asked 2022-08-30

For a given function is there a general procedure to find an initial value for ${x}_{1}$ such that Newton's method bounces back and forth between two values forever?

asked 2022-09-23

Consider the function $f(x,y)=5{x}^{2}+5{y}^{2}-xy-11x+11y+11$. Consider applying Newton's Method for minimizing f. How many iterations are needed to reach the global minimum point?

asked 2022-09-07

Find the cube root of 9, using the Newton's method.

asked 2022-10-18

Using Newton's method below:

${x}_{n+1}={x}_{n}-\frac{f({x}_{n})}{{f}^{\prime}({x}_{0})}$

using this chord formula where the chord length $c$ is $1$ cm:

$c=2r\mathrm{sin}\frac{\theta}{2}$

supposing the radius is $1.1$ cm and the angle $\theta $ is unknown, show the iterative Newton's Method equation you would use to find an approximate value for $\theta $ in the context of this problem (using the appropriate function and derivative).

${x}_{n+1}={x}_{n}-\frac{f({x}_{n})}{{f}^{\prime}({x}_{0})}$

using this chord formula where the chord length $c$ is $1$ cm:

$c=2r\mathrm{sin}\frac{\theta}{2}$

supposing the radius is $1.1$ cm and the angle $\theta $ is unknown, show the iterative Newton's Method equation you would use to find an approximate value for $\theta $ in the context of this problem (using the appropriate function and derivative).