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Martin Thoma 11 years ago
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documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex

@@ -419,6 +419,10 @@ take the same approach as in Equation \ref{eq:minimizingFirstDerivative}:
        &= \underbrace{\left (2 f(x) - 2 y_p \right ) \cdot f'(x)}_{\text{Polynomial of degree 5}} + \underbrace{2x - 2 x_p}_{\text{:-(}}
 \end{align}
 
+\todo[inline]{Although general algebraic equations of degree 5 don't
+have a closed-form solution, the special structure might give the
+possibilty to find a closed form solution. But I don't know how.}
+
 \subsection{Number of points with minimal distance}
 As there is an algebraic equation of degree 5, there cannot be more
 than 5 solutions.