Unfortunately numerical analysis is a very boring tedious subject and is usually avoided. One DOD application I worked on used trig to find the intersections of annuli on the surface of a sphere. The initial results were nonsense so I increased the floating size from "short" to "long" and then the results came out as I expected them to. As an "evaluation" application it was never fielded. Fielded applications should require all sorts of tests for numerical stability, though from working in that area I get the impression that many flight control or weapon control systems that use floating point arithmetic are fielded without any proper numerical analysis (though some are.)
Since Numerical Analysis is boring and the problem cases from floating computation in the wrong order are arcane, have there been any attempts to automate the conversion from real mathematical expressions to appropriately sized computer numbers and to properly sequence the order of evaluations such that noise doesn't predominate?
Your advocacy of some sort of super floating point numbers seems in part to be an easy-way-out approach like I above adopted above - bigger or better number representations will reduce noise. But it really doesn’t deal with the ultimate goal of how to avoid generating noise in the first place.
[ Yes I have numerically analyzed computations but I find it very tedious. And it much easier to do in a fixed point representations ]
posted by Monkey Boy
August 12, 2009
About once a month at Sigma Xi headquarters, we liven up the lunch hour with an American Scientist Pizza Lunch talk. In these informal lectures, scientists describe new research to nonscientists. The series is light on jargon but heavy on solid science. Each Pizza Lunch offers an in-depth look at its subject, whether it's bedbugs or the smart grid. Click below to read about and download these talks -- and to subscribe!
JSTOR, the online academic archive, now contains complete back issues of American Scientist from its inception in 1913 (as Sigma Xi Quarterly) through 2005.
The table of contents for each issue is freely available to all users; those with institutional access can read each complete issue.
View the full collection here.