inequality values
in [Fortran]
|
From: Elaheh on 27 May 2010 03:24 I have two matrices (a,b). if I show determinant of matrix with det, I will have: Det([transpose(a)][b]) = Det([transpose(b)][a]) I have written a code with Fortran90 to calculate above term, but values of both sides of equation are different in some digits (scalar information takes 8 byte). This inequality makes error. How can I get same values? Thanks in advance
From: Arjen Markus on 27 May 2010 03:38 On 27 mei, 09:24, Elaheh <elaheh.ad...(a)gmail.com> wrote: > I have two matrices (a,b). if I show determinant of matrix with det, > I will have: > Det([transpose(a)][b]) = Det([transpose(b)][a]) > I have written a code with Fortran90 to calculate above term, but > values of both sides of equation are different in some digits (scalar > information takes 8 byte). This inequality makes error. How can I get > same values? > > Thanks in advance You can't. Not in general, that is. This is fundamental to the finite precision arithmetic we have to deal with. You can get close, but that is not the same. Here is a simple example: Mathematically, (1.0e20 + 1.0) - 1.0e20 = (1.0e20 - 1.0e20) + 1.0 = 1.0 But due to the finite precision (take 10 digits for instance): (1.0e20 + 1.0) - 1.0e20 = (approximately) 1.0e20 - 1.0e20 = 0.0 and (1.0e20 - 1.0e20) + 1.0 = 0.0 + 1.0 = 1.0 Things get worse if you have many computations, like with determinants. Hope this clarifies the problem. Regards, Arjen (1.0
From: mecej4 on 27 May 2010 07:48 Elaheh wrote: > I have two matrices (a,b). if I show determinant of matrix with 'det', > I will have: > Det([transpose(a)][b]) = Det([transpose(b)][a]) > I have written a code with Fortran90 to calculate above term, but > values of both sides of equation are different in some digits (scalar > information takes 8 byte). This inequality makes error. How can I get > same values? > > Thanks in advance On your electronic calculator, carry out the following calculation exactly as shown, see what the result is, and try to explain why it came out that way: (4.0/3.0 - 1.0)*3.0 - 1.0 --mecej4
From: Gib Bogle on 31 May 2010 00:29 mecej4 wrote: > Elaheh wrote: > On your electronic calculator, carry out the following calculation exactly > as shown, see what the result is, and try to explain why it came out that > way: > > (4.0/3.0 - 1.0)*3.0 - 1.0 My electronic calculator (Aurora SC190) gave the answer 0. I can't explain why it came out this way.
From: JWM on 31 May 2010 01:12
On Sun, 30 May 2010 22:29:38 -0600, Gib Bogle <g.bogle(a)auckland.no.spam.ac.nz> wrote: > mecej4 wrote: >> Elaheh wrote: > >> On your electronic calculator, carry out the following calculation >> exactly >> as shown, see what the result is, and try to explain why it came out >> that >> way: >> (4.0/3.0 - 1.0)*3.0 - 1.0 > > My electronic calculator (Aurora SC190) gave the answer 0. I can't > explain why it came out this way. Maybe because it's set to display the answer in fixed-point format? |