QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: PolterQuoteOriginally posted by: Traden4AlphaIsn't measurement error in most data much worse than round-off error in floats and doubles?And let's not forget modeling error and approximation error:http://www.johndcook.com/blog/2011/11/0 ... eProfessor
Nick Trefethenif computers were suddenly able to do arithmetic with perfect accuracy, 90% of numerical analysis would remain importantSo true!One might say that floating-point round-off error is a kind of model error. The "real" system has Real numbers but the model uses floats, doubles, etc.Not sure if I would agree. I think it fits into category (B) here below.Errors in given input data (D)Round-off errors during computation (B)Truncation errors Simplification of the mathematical model (A)Human and machine errors (C) What I find tricky is to determine if it is A or B. In the past -when computers ran on steam - backward error analysis was part of 1st year numerical analysis courses (
analysis just tells us how big the error is. I would consider undocumented code as an error in class C. Another scenario is the model (A) cannot handle the range of values in (D). We might jump to the conclusion that it is caused by (B).You may be right or it may be a fuzzy line.To me, the analytic model is an approximation of the real system and the numerical/computational model is an approximation of the analytical model. The numerical/computational model contains model errors due to assuming that floats are Real numbers just as the analytic model assumes that the analytic variables accurate reflect the real system.But I do agree that round-off error has a different character than some other modeling errors.