how to solve a fourth degree polynomial for x / polyval for x

I've designed an app that is able to extrapolate the y at any given x. To do this i've used polyfit to generate a fourth degree polynomial, based on testdata. It works perfectly to find y when x is given.

Now i would like to reverse it so that I can enter a y, and get the x-value for the same polynomial. Doesn't MatLab have a built-in function for this?

Below is shown the code I've used to generate the polynomial and find the y-value

y_sample=[18.5610 21.298 27.531 36.8 51.221];   % test data              
x_sample = (0.25:0.25:1.25);                    % x-values for test data
p = polyfit(x_sample,y_sample,4);               % fourth degree polynomial
y_value = polyval(p,X)                          % THIS IS THE LINE I WISH TO BE SOLVED FOR X

I know 4th degree isn't optimal for this example, but it is needed for some of the other uses of the function.

Answer 1

[Ameer Hamza]

What about reversing the interpolation

y_sample=[18.5610 21.298 27.531 36.8 51.221];   % test data              
x_sample = (0.25:0.25:1.25);                    % x-values for test data
p = polyfit(y_sample,x_sample,4);               % fourth degree polynomial
x_value = polyval(p,Y)

[Kenneth Carlson]

I've been stuck at this longer than i'd care to admit. Thank you so much for this simple solution.

[Ameer Hamza]

I am glad to be of help!

Yes, some time overthinking a problem can prevent from seeing an obvious solution. Following is an alternative solution. It is a bit more computationally expensive (if you are not going to run it several times, then it is not a problem), but the good thing is that it is exactly reversible. For example, in my above code, if you take the output x_value and interpolate it again, you will not exactly get Y. However, the following will work give an exact value

y_sample=[18.5610 21.298 27.531 36.8 51.221];   % test data              
x_sample = (0.25:0.25:1.25);                    % x-values for test data
px = polyfit(x_sample,y_sample,4);              % fourth degree polynomial
py = polyfit(y_sample,x_sample,4);

y_value = @(X) polyval(px, X);

y = 20; % let you need to interpolate at this point
x_interp = polyval(py, y);
x_fsolve = fsolve(@(x) y_value(x) - y, x_sample(1));

Now try getting y from these x values

>> y_value(x_interp)
ans =
   19.6410
>> y_value(x_fsolve)
ans =
   20.0000

[Kenneth Carlson]

Unfortunately it requires the optimization toolbox, which I don't have avalible. I will have to settle for the "not as precise" result, and see how it works out for now.

Thanks again though.

[Steven Lord]

Since you're trying to find a zero of one equation in one unknown you don't actually need fsolve here. fzero is in MATLAB and can handle this problem.

Answer 2

[Mohlouwa Joseph BOTMAN]

Consider the two polynomials 3 2 p(s) = s + 4s +5s + 2 and q(s) = s +C

1.1 Determine p(s)q(s) based on the simulation software.

(3)

1.2 Determine the poles and zeros of

( )

( )

( )

q s

G s

p s

= based on the simulation software

[Steven Lord]

Since this is not related to the original question, you should post this as a separate question. When you do, since this sounds like a homework assignment please show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.