Timeline for A reference request for linear iterations with "rounding"
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2010 at 4:58 | answer | added | Aaron Meyerowitz | timeline score: 0 | |
| Nov 8, 2010 at 19:24 | comment | added | Aaron Meyerowitz | I recall a problem floating around Ohio State a few decades ago. It involved a rounded version of a 60 degree rotation (using both round up and some round down) which was a bijection on ZxZ. The question was if all orbits were finite. Ive not managed to recreate it so far. | |
| Nov 8, 2010 at 16:57 | answer | added | Rod Carvalho | timeline score: 4 | |
| Oct 29, 2010 at 7:03 | answer | added | sleepless in beantown | timeline score: 1 | |
| Oct 29, 2010 at 6:54 | comment | added | sleepless in beantown | @Joseph-O'Rourke, it's also equivalent to what must happen in fixed-digit or limited precision representation of floating point digits in any computerized simulation of any dynamical systems. The numerical simulation is only correct up to a certain number of digits, and the imprecision can build up rather quickly depending upon the variance of the elements of the matrix. Rounding occurs in every floating-point representation using a fixed number of bits; it just occurs at smaller magnitudes with larger number of bits used for the mantissa. | |
| Oct 29, 2010 at 0:57 | comment | added | Joseph O'Rourke | One keyphrase that might be remotely related is iterative rounding, used in multiobjective optimization problems to obtain approximations. | |
| Oct 29, 2010 at 0:43 | comment | added | sleepless in beantown | What are the restrictions on $A, B,$ and $x(0)$ in the type of system which you do already understand? What physical system are you modeling? (My question is merely out of curiousity; sometimes, however, knowing the underlying system being modeled helps to constrain some of the equations and assumptions about the dynamical equations...) | |
| Oct 29, 2010 at 0:04 | comment | added | alex | I did not say this in the question, but I have a very specific system of this form which I want to analyze, and whose behavior I do understand when $x,A,B$ are in $R^3$. I'm looking for any related work out there. Its true that a complete classification of the behavior of such systems for all dimensions seems like too much to hope for. | |
| Oct 29, 2010 at 0:00 | comment | added | alex | @Joseph O'Rourke - no, I don't. | |
| Oct 28, 2010 at 23:49 | comment | added | Joseph O'Rourke | Do you understand its behavior when $x$, $A$, and $B$ are all just real numbers, rather than vectors and matrices? Its behavior already seems quite complicated. | |
| Oct 28, 2010 at 22:26 | history | asked | alex | CC BY-SA 2.5 |