how to decrease precision

Juan Getino (view profile)

on 17 Feb 2019
Latest activity Edited by John D'Errico

on 17 Feb 2019

John D'Errico (view profile)

I am trying to show to my students examples on the effect of rounds error when performing Gauss elimination without pivoting. This question is very easy with Maple, simply by fixing the numbers of desired digits with Digits:=4, for instance. In this way, I can show the errors appearing in the solution when performing Gauss elimination without pivoting.
But I do not know haw to proceed in Matlab, I always get the exact solution.

Rik

Rik (view profile)

on 17 Feb 2019
Are you using a numerical method, or are you using the symbolic toolbox? In the case of the first, you can use this:
digits=4;
data=(10^digits)*round(data/(10^digits));% round to n digits

R2018a

John D'Errico (view profile)

on 17 Feb 2019
Edited by John D'Errico

John D'Errico (view profile)

on 17 Feb 2019

You cannot tell MATLAB to use an arbitrary lower or higher precision. At most, you can work in single precision instead of double. But even there, you need to be careful, as all numbers by default are ALWAYS doubles. So it would be possible to introduce doubles into the problem, thus to accidentally suddenly start working in double precision. Luckily, singles tend to propagate.
A = single(2) + double(3)
A =
single
5
Can you do more than that? This is difficult if you choose to force yourself to work with the standard MATLAB numeric data types. I suppose you could download my HPF toolbox from the file exchange. So, in HPF, if I want to force all computations done in that tool to use EXACTLY 7 decimal digits, then I could do this:
DefaultNumberOfDigits 7 0
x = hpf(pi)
x =
3.141593
That will cause all numbers created as HPF to display and store only 7 digits, with no hidden (i.e., guard) digits carried in the background, and that setting will persist until you change it, even if you exit MATLAB and restart.
And, of course, you can also work with the symbolic toolbox.