Discrepancy between normal computations and the "subs" function results.

I'm dealing with quadratic equations, so i have something like:

k1 * x1^2 + k2 * x2^2 (quadratic terms) + k3 * x1 * x2 (mixed term) + k4 * x1 + k5 * x2 (linear terms) + k6 (constant)

Note: the equations im dealing with are way more complicated, they have more quadratic, mixed and linear terms. Im just simplifying the equation to explain the problem.

I know both the coefficients (k1, k2, ..., k6) and the unknown parameters (x1, x2). So i just have to substitue these values in the equation and get the result.

The problem is this:

If i use the "subs" function (result = subs(equation, x, unknown_parameters_values) i get one result. Note that "equation" is a symbolic function of course.

If i compute the products and sum them i get another result, which differs a lot from the one i get from using the "subs" function.

I know it is an apporximation problem, but is there a way I can fix it? Also what result is more accurate, the first one where i use the "subs" function or the one where i compute the terms one by one? I would like to get at least 2 similar results.

Thank you for your help.

[Paul]

Just to be clear, is "compute the products and sum them" all being done using Symbolic sym objects?

For example, suppose we have

syms k1 x1 x2
equation = k1*x1^2 + k3*x1*x2

Can you show how you're executing the subs command and how you would compute the products and sum them for representative values of k1, k3, x1, and x2.

[MDL]

Sorry I forgot to specify that. I have the coefficents k and the unknown_values stored in 2 arrays of double.

So i have something like:

k = [1 2 3 4 5 6];
uv = [10 20];
result = k[1]*uv[1]*uv[1]+k[2]*u[2]*u[2]+...

The result i get this way is very different from the result i get this way:

syms x[2 1];
equation = k1*x1^2 + ...
result = subs(equation, x, uv);

In the symbolic equation are included the coefficients "k". The only symbolic terms are x1 and x2.

[Paul]

It would be very helpful to provide a simple example of working code, otherwise we are just guessing. Is this what the workflow looks like?

k = [1 2];
syms x [2 1];
equation = k(1)*x(1)^2 + k(2)*x(2)^2;
uv = [10; 20];
y1 = subs(equation,x,uv)

y1 = 

900

y2 = k(1)*uv(1)*uv(1) + k(2)*uv(2)*uv(2)

y2 = 900

[Matt J]

which differs a lot from the one i get from using the "subs" function.

Please also elaborate on "differs a lot". What is the relative error?

[Dyuman Joshi]

@MDL Please attach the code you are working with or relevenat portion of it.