Talk:Numerical integration/Gauss-Legendre Quadrature: Difference between revisions

: This is a two-fold problem. In principal, the higher order you go, the better you can decompose your function into a sum of polymials, so with infinite order you can get exact result -- on paper. In a computer, every time you do math with a floating point number, you get an error due to precision (up to <math>\sim 10^{-16}</math> of the value with IEEE 64 bit in general), and later you use the result to do more math, the error propagates and gets larger and larger. Higher orders require a lot more arithmetic operations (about <math>O(n^2)</math> I think), so at some point, the precision error dominates and more terms only make results worse. --[[User:Ledrug|Ledrug]] 07:39, 28 June 2011 (UTC)

:: Though, of course, you could use something other than ieee floating point to represent your numbers -- perhaps arbitrary precision rationals? --[[User:Rdm|Rdm]] 11:06, 28 June 2011 (UTC)