MATLAB: How to decrease precision

MATLABprecisionround errors

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.

Thank you in advance.

Best Answer

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.

https://www.mathworks.com/matlabcentral/fileexchange/36534-hpf-a-big-decimal-class

And, of course, you can also work with the symbolic toolbox.

Related Solutions

MATLAB: Solve a system of algebraic equations by Gauss elimination using two significant digits

I'm sorry. But you cannot "set" MATAB to store only two significant digits, or any fixed number of significant digits, other than double or single precision.

I suppose you could round each result to two significant digits after EVERY individual computation. I'm not at all sure why you wish to bother doing such a ridiculous thing anyway, as it would yield complete garbage for results almost always.

The easiest way, IF this is not a homework assignment, would be to use my HPF. tool, which CAN be used to specify a number of decimal digits in all computations. You would need to download and install the toolbox from the File Exchange. Then issue this command:

defaultNumberOfDigits 2 0

So now all computations using HPF numbers will be done in only 2 digits of precision.

p = hpf(pi)
p =
3.1e0
p*3
ans =
9.4e0

So you could easily force all computations done using HPF to be in 2 decimal digits of accuracy. Now just define all of your variables as HPF numbers, and execute the Gauss elimination. Again, a complete waste of time unless it is a homework assignment, and you were forced to do it.

If this is for homework, then do the Gaussian elimination by hand, carrying two digits at each step.

Finally, if your question is only how to retain only two significant digits at the VERY end, WHY? Another silly goal. However, you could just use the round function on the final result.

MATLAB: How to get more than 49 digits of pi in a string

You could always download my HPF toolbox from the file exchange. It will provide 500100 digits of pi.

P = hpf('pi',500000);
cp = disp(P);
numel(cp)
ans =
      500001
      
cp(1:1001)
ans =
    '3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198'

So 1000 digits of pi, plus a decimal point.

As I recall, I even computed those digits using HPF itself just to test the tool, and verify it was working correctly. I'm not sure which series I used, but there are many good ones out there if you look carefully. You do need to be working with a tool that can handle high precision arithmetic. A double will not suffice.

Be careful with the last digit reported to make sure it was not rounded. For example, if you do this:

vpa(sym('pi'),1000)

the last 10 digits reported are ...9216420199

However, the true digits of pi in that vicinity run as: ...9216420198938095...

So the last digit reported by vpa is actually rounded up to a 9.

Best Answer

Related Solutions

MATLAB: Solve a system of algebraic equations by Gauss elimination using two significant digits

MATLAB: How to get more than 49 digits of pi in a string

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