Timeline for Dividing a sphere into thirds with two planes
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2015 at 3:42 | history | edited | Ross Millikan | CC BY-SA 3.0 |
add info
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| Apr 3, 2015 at 3:15 | comment | added | Patrick Shambayati | Do you mind posting the first few fixed-point iterations from your Excel sheet? I want to get an idea of how quickly we coverge | |
| Apr 3, 2015 at 3:12 | comment | added | Ross Millikan | Sorry, the last sentence should have said the error is reduced by about a factor $|f'(y)|$ each step. | |
| Apr 3, 2015 at 1:39 | comment | added | Ross Millikan | Yes, it is called fixed-point iteration. You find some function $f(x)$ such that the solution to your problem satisfies $x=f(x)$ If $f(x)$ is smooth enough, $y$ is the solution and $|f'(y)| \lt 1$, iteration will converge to the root as long as you start close enough. The smaller $f'(y)$ is, the faster it will converge. You want to put slowly varying terms into $f(x)$. The error is reduced by a factor of about $|f(y)|$ each step. | |
| Apr 3, 2015 at 1:34 | comment | added | Patrick Shambayati | Thank you! Is there a common name for the iterative method you used? | |
| Apr 3, 2015 at 1:21 | history | answered | Ross Millikan | CC BY-SA 3.0 |