Question

For which $k$ we have: $|x_k-\alpha|\le10^{-16}|\alpha|$ where $\alpha$ is a solution of the equation $10x-\sin x=3$?

score 30 · Answer 1 · 2020-05-08 21:32:05

For which $k$ we have: $|x_k-\alpha|\le10^{-16}|\alpha|$ where $\alpha$ is a solution of the equation $10x-\sin x=3$?

score 166 · Answer 2 · 2026-04-11 17:07:11

166

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104

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score 72 · Answer 4 · 2026-04-17 12:59:05

72

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Iterates of $\frac{\sqrt{2}x}{\sqrt{x^2 +1}}$ converge to $\text{sign}(x)$.

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score 61 · Answer 5 · 2026-03-25 16:03:06

61

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score 92 · Answer 7 · 2026-03-25 17:40:24

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score 80 · Answer 8 · 2026-04-12 05:54:13

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score 23 · Answer 12 · 2026-03-25 15:58:28

23

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score 29 · Answer 15 · 2026-03-25 17:40:20

29

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List Question

For which $k$ we have: $|x_k-\alpha|\le10^{-16}|\alpha|$ where $\alpha$ is a solution of the equation $10x-\sin x=3$?

Fractal construction and IFS (iterated function system): defining a specific construction with IFS

How is this interesting fractal generated?

Iterates of $\frac{\sqrt{2}x}{\sqrt{x^2 +1}}$ converge to $\text{sign}(x)$.

Can a self-similar shape not be a polytope yet have a non-fractal boundary?

Generalization of the sliding ladder problem

Do the self-similarities of a fractal function govern its convergence properties?

Does this fractal mapping have a name?

How to find the limit to infinity of the iterative function used in the Mandelbrot set with a fixed C.

For a convergent iterated function, is the distance between the nth iteration and the fixed point always decreasing as n increases?

Loops in a binary iterated function system

Fixed point convergence of vector scheme

How can i solve this optimization problem effectively?

Symmetry of King's dream fractal (orbit of a 2-dimensional iterated function system is a parallelogram?)

$\mathbb K_3$, attractor of a pair of contractions

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