Increase the precision of the finding roots

Hi I have written a m file in which I'm trying to find ROOTs of a polynomial of of 6'th degree.I do this in a cycle using "do" because a parameter in the coefficients of the polynomial have to change in each step and the ROOTs should be calculated and saved for further mathmatical calculations. The problem is that in this exact case of mine the real part of each root is very small so that matlab ignores them in some steps and doesnt ignore in other cases(by cases I mean change of that parameter).and this cause the results to oscillate.I know that this real part despite it's smallness is'nt zero. HOW CAN I INCREASE THE PRECISION IN THIS EXACT CASE? thanks for your attention.

Answer 1

[Walter Roberson]

If the function uses its own precision, then we would need to see the function in order to see how to increase the precision. There is not just one method for doing extended precision calculations.

If you have access to the symbolic toolbox, consider using that for the calculations.

Note: in any finite precision calculation scheme, there are calculations that will oscillate in the manner you describe.

[Atta Oveisi]

thanks and yes I have access to symbolic toolbox.I will try it.

[Walter Roberson]

In theory, MuPAD should be able to provide numeric solutions for 6th degree polynomials, to any desired precision according to the Digits setting. In practice, I have seen a number of cases where it left the polynomials in symbolic form and said that was the best it could do; there is some evidence that in one of the most recent MATLAB releases that that situation might have been greatly improved.

[Dima]

Try

roots(conv(conv([1 -2 1],[1 -2 1]),[1 -2 1]))

There is still a problem with multiple roots.

[Walter Roberson]

You are correct that roots does not do a good job on that . solve(poly2sym()) of the vector produces exact solutions though .

Answer 2

[Andrew Newell]

Unless this is an exercise, you could just use roots to solve your problem.

[Atta Oveisi]

what do you mean by "exercise"?

It's not an execise.this is part of a procedure that finds the natural frequencies of a circular cylinderical panel an a pasternak fundation.and if that real parts become zero the eigen functions of the system changes from bessel of first kind to the modified bessel function.and this change of the eigen functions leads to wrong natural frequencies.

thanks.

[Andrew Newell]

I'm just saying that if you don't have any compelling reason to write the m file yourself, you'd be better off using the MATLAB function.

[Atta Oveisi]

I myself want to use "root" but the roblem is this function use it's own number of precision.my question is how to increase this.