MATLAB: How to find the value for X for given Y on a function

formulastudentMATLAB

Hello everybody. I have a polynomial function "y = p1*x^n + p2*x^(n-1) + … pn". This function was defined using the comando "Polyfit" based on some points, resulting in a fourth order equation. Then this equation was integrated, resulting in a fifth order equation. As the value of "y" was previously calculated, I need to know the value for "x". How can I do that?

Thanks.

Best Answer

With the roots() function.

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MATLAB: How to fit custom polynomial equation

You could download polyfitn from the file exchange.

But if you already know how to use the curve fitting toolbox, then just specify a custom equation of the desired form. Something like this:

modelform = fittype('p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y',...
    'coeff',{'p00','p10','p01','p20','p11','p02','p30','p21'},...
    'indep',{'x','y'},'depend','z');

It will be treated as a nonlinear model internally as a function of the parameters, but since all of the coefficients actually do enter linearly, they will be easy to fit. fit should have no problems.

MATLAB: Soving polynomial equation with negative powers

If the last term is Z * x^(-P), then multiply the equation by x^P, transforming it into

a*x^(P-1) + b*x^(P-2) + c*x^(P-3) + .... Z = 0

then you can use roots()

If you think about this for a second, you can see that you can skip the roots() step if your coefficients are arranged in the right order.

Best Answer

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MATLAB: How to fit custom polynomial equation

MATLAB: Soving polynomial equation with negative powers

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