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
JSTOR, the online academic archive, contains complete back issues of American Scientist from 1913 (known then as the 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.
An early peek at each new issue, with descriptions of feature articles, columns, and more. Every other issue contains links to everything in the latest issue's table of contents.News of book reviews published in American Scientist and around the web, as well as other noteworthy happenings in the world of science books.
To sign up for automatic emails of the American Scientist Update and Scientists' Nightstand issues, create an online profile, then sign up in the My AmSci area.