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Re: calculation of exp(200)
Posted:
Jul 9, 2014 12:12 PM


"kumar vishwajeet" <kwzeet@gmail.com> wrote in message news:lphu22$5i$1@newscl01ah.mathworks.com... > "Nasser M. Abbasi" wrote in message <lpfj5e$4c4$1@speranza.aioe.org>... >> On 7/7/2014 8:26 PM, kumar vishwajeet wrote: >> > I want to find exp(N) where N can range from 0 to 200. >> >Is there any method to calculate it with good accuracy? >> >> as James said, you can use vpa >> >> vpa(exp(sym(200)),500) >> 7225973768125749258177477042189305697356874428527 >> 31928403269789123221909361473891661561.9265890625 >> 7055746840204310142941817711067711936822648098307 >> 7273278800877934252667473057807294372135876617806 >> 9702350324220401483115192088442120622525378469924 >> 9272881421981093552839024711140014485905504285329 >> 2850053281888896583514044902234770562940736477036 >> 9022153799888245922895391403712478563813079673045 >> 5316370477078232246232166391756343572294659379732 >> 9550687822348546666476886365318979823972170480437 >> 40943587594 >> >> But you have to do all the rest of the computation >> is syms land, otherwise what is the point of >> getting this accuracy if you can't use it in >> numerical matlab. >> >> >> > Actually I have a matrix whose elements range from exp(200) to exp(200).
Is your matrix a double precision matrix or a symbolic matrix?
>The matrix is ill conditioned with conditioning number of 10^167.
So ... if you're doing ANYTHING in double precision with this matrix, you're getting garbage.
http://en.wikipedia.org/wiki/Condition_number
"As a general rule of thumb, if the condition number is 10^k , then you may lose up to k digits of accuracy on top of what would be lost to the numerical method due to loss of precision from arithmetic methods." [replaced images with text.]
By this guideline, you're losing roughly 167 digits of accuracy for the numbers you know to roughly 16 digits.
> I am calculating determinant of this matrix. MATLAB gives it in the > 10^13. The matrix is posted in the following link. > http://math.stackexchange.com/questions/859597/determinantofanillconditionedmatrix/859614#859614 > So, I was just wondering whether to rely on this calculation of > determinant or not.
That looks like you're trying to perform the computations in double precision, in which case I would try not to have anything to do with this matrix at all.
What is the underlying problem that you're trying to use this problem to solve? There may be a way to solve that problem that doesn't require creating a matrix whose elements span 200+ orders of magnitude.
 Steve Lord slord@mathworks.com To contact Technical Support use the Contact Us link on http://www.mathworks.com



