Talk:Safe addition: Difference between revisions

: I am not sure, if this answers your question. Addition of intervals is defined as [''a'', ''b''] + [''c'', ''d''] = [''a'' + ''c'', ''b'' + ''d'']. With +↓ and +↑ operations its machine implementation becomes [''a'' +↓ ''c'', ''b'' +↑ ''d'']. As for error (rather uncertainlyuncertainty) of the result obtained using interval arithmetic, it is not a simple issue. The result's width grows under the assumption of the worst case scenario. That is, assuming all intervals involved in computations independent. The intermediate results are often dependent, so the inputs, etc. Therefore in many cases the result can be improved in terms of interval width. A simple illustration of the case. Consider interval expression [1, 2] x [1, 2]. According to the interval arithmetic, the result is [1, 4]. But that is when [1, 2] and [1, 2] are fully independent. If they were ''same'' (correlated), we could multiply [1, 2] by 2, and get a two-fold narrower result [1, 2] * 2 = [2, 4]. --[[User:Dmitry-kazakov|Dmitry-kazakov]] 08:46, 19 August 2009 (UTC)