Questions tagged [fixed-point-iteration]
126 questions
2
votes
0 answers
Rate of iteration convergence
For the iteration
$$x_{n+1}=f(x_n)\equiv \sin(x_n) \text{ with initial value } x_0=1,$$
I know it converges since $x_{n+1}\le x_n$ for all $n$ and the limit is zero, so the iteration converges to zero, but how do I know the rate of convergence?…
bowen.jane
- 361
0
votes
2 answers
Minimizing the norm via fixpoint iteration
I have to calculate this in Matlab:
$\operatorname{argmin}_{\lambda} \|a-\lambda b\|_1$,
where $a$ and $b$ vectors in $\mathbb{R}^n$. How can I minimize this in Matlab with a fixpoint iteration? I have to transform it to in equation like…
brian
- 43
0
votes
1 answer
Fixed point iteration on open interval proof
I need to prove that if equation $x = g(x)$ has solution $x^*$ and $g$ is contracting in open interval $(x^* - d, x^*+d)$ where $d > 0$ then for every $x_0$ in $(x^*-d, x^*+d), x_n \mapsto x^*$.
I don't know where to start. I already have a proof…
Marko Taht
- 271
0
votes
0 answers
Fixed-Point Iteration: For what constant does it converge?
Consider the equation $f(x)=0$ where $f$ is a $C^1$ function which has a root $x^*$. We can rewrite the equation as $x=g(x)=x-cf(x)$ for some constant $c$. We are asked to find the values of $c$ for which the iterative method $x_{n+1}=g(x_{n})$…
user92596
0
votes
1 answer
Limit of iteration convergence
The iteration as given to me is this:
$x_{n+1}=F(x_n)=sin(x_n), x_0=1$
so I think that the start of the iteration would look something like this:
$x_0=1$
$x_1=sin(1)=.841$
$x_2=sin(sin(1))=sin(.841)=.7456$ and so on.
My professor said this…
bowen.jane
- 361