MATLAB: How to find the roots of a sum of divisions of polynomials

polynomial calculus

How can I find those x values in which this function becomes f(x)=0?

I have 4 vectors of length N: A, B, C, D, and

f(x) = sum( ( x*A_i – B_i ) / ((x*C_i – D_i)^3) )

Best Answer

Multiply by

prod (x*C_i - D_i)^3

and determine the roots of the resulting polynomial of degree 3*(N-1)+1 using the "roots" command.

You might want to use symbolic computations in advance using expand, collect, and subst to get the numerical coefficients of this polynomial.

Related Solutions

MATLAB: Find the coefficient of polynomial

Use polyfit():

coefficients = polyfit(x, fx, 3);
D = coefficients(1);
C = coefficients(2);
B = coefficients(3);
A = coefficients(4);

MATLAB: Qfunc() division

Notice that you are dividing the outputs from qfunc using only 4 decimal points to verify your analytic result. Actually, MATLAB is showing a short visualization format when you type a1, a2 and P.

If you type format long and show the values for a1 and a2 you will notice that you are getting different results because you are truncating a1 and a2 to 4 decimal points when verifying your results:

0.0228/0.0668 = 0.3413

but actually, the correct result is:

>> P = a2/a1
P =
     0.340534126802047

since a1 and a2 have many more decimal places...

Best Answer

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MATLAB: Find the coefficient of polynomial

MATLAB: Qfunc() division

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