MATLAB precision

Question

How can I implement quadruple precision (128 bit arithmetic) in MATLAB while solving a Matrix eigenvalue problem ?

I am trying to solve a linear stability analysis p

Answer 1

I do have a general precision floating point arithmetic toolbox in MATLAB, that does not require the symbolic toolbox. It is available on the File Exchange now. As an example, in 200 digits of precision...

>> X = hpf('1.2',200)
X =
    1.2

>> X^723 - 2
ans =
    1770275636625441478440184064843963160282702377364043536065.674784028
335311702907341138106304578079399191891193908698215227428501441099262538
4031886249461115861966367898404170725299823585166135087107488           

If you wish to do all of your arithmetic in 200 digits of precision when HPF numbers are employed, then just specify that as the default.

>> DefaultNumberOfDigits 200
>> hpf('pi')
ans =
    3.141592653589793238462643383279502884197169399375105820974944592307
816406286208998628034825342117067982148086513282306647093844609550582231
7253594081284811174502841027019385211055596446229489549303819           

HPF is not a true variable precision tool by design since it works in a fixed number of digits. It is reasonably efficient up to a few tens of thousands of digits. So to get 100 digits of exp(pi), this takes about 1/4 of a second.

>> timeit(@() exp(hpf('pi',100)))
ans =
   0.2643

Trig functions too. Here 1000 digits of the sin(pi). It should be zero of course.

>> tic,sin(hpf('pi',1000)),toc
ans =
    0
Elapsed time is 0.201679 seconds.