Timeline for Are there ill-conditioned problems in infinite precision arithmetric?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2011 at 6:50 | vote | accept | alext87 | ||
| Jun 1, 2011 at 21:41 | comment | added | David Harris | @Federico: GPU's are designed for graphics (i.e. games), not scientific computing. GPU manufacturers typically add double-precision support specifically to accommodate scientific computing. Current or forthcoming x86 chips will have extension for quad-precision. (And of course there are multiprecision libraries). | |
| Jun 1, 2011 at 21:16 | history | edited | Federico Poloni | CC BY-SA 3.0 |
small clarification in the last sentence
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| Jun 1, 2011 at 21:10 | comment | added | Federico Poloni | To support the point "arithmetic precision is not so much relevant with respect to errors in the data", I can add that in the last 20 years the precision used in scientific computation hasn't increased, despite the huge advances in computational power. In fact in some cases it has decreased, since GPU architectures often support only single precision. So, while 640k are not enough for anybody, apparently 16 digits are. | |
| Jun 1, 2011 at 20:10 | comment | added | David Harris | Federico's answer is good. I would just like to add that if a problem is ill-conditioned (in infinite precision arithmetic), then necessarily it will be algorithmically unstable (in finite precision arithmetic). The reason is that the initial data will need to be rounded to the nearest floating-point-representable number. Even if the algorithm commits no further errors, it will still have large error because of this initial rounding error. | |
| Jun 1, 2011 at 19:34 | history | answered | Federico Poloni | CC BY-SA 3.0 |