Posted by mathstudent on Friday, April 18, 2008 at 3:06pm.
I'm trying to follow a research paper
The paper shows an equation to minimize. That makes perfect sense. Then, the paper says:
"The optimal solution to the least squares problem [above] is found by differentiation as a solution of a linear system of equations."
I am very familiar with traditional linear algebra least squares:
y = xb + e
solve for coefficients b by:
b = (x^T * x)^1 * x^T * y
I understand the equation to be minimized but I don't understand the formulas that follow, and I think the paper is using some alternative least squares approach that I am not familiar with. It doesn't look like the paper is doing regular least squares (like I know). Any ideas what the paper is referring to? How do you use differentiation as a solution to a linear system of equations?

math  Carmen, Monday, April 21, 2008 at 12:30am
Differentiation is used when the equation is nonlinear. To parameterize the equation, partial derivatives are used to construct the design matrix (in your case, that would be the b matrix.) x would be the unknown vector, e would be the residual vector and y would be your observation vector.
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