Category Archives: Applied mathematics

Least squares in a non-ordinary sense

Simple ordinary least squares regression (SOLSR) means the following. Given data , , find a line in represented by that fits the data in the following sense. The loss of each data point to the line is       … Continue reading

“Useless” Circle Properties: The Green Flash In Mathematics

Since F.4 I’ve been thinking long and hard about real-life applications of circle properties. Why do we study them in secondary school anyway? Someone told me they’re used in designing cylindrical structures, but I couldn’t find a satisfactory book or website that … Continue reading

Polynomial Optimization 3: Why do we need generalize?

It has been a while since the last post. Let us recall what we have done. We study the unconstrained polynomial optimization problem ()           where is a real polynomial. This problem is equivalent to () … Continue reading

AM-GM-HM Inequality: A Statistical Point of View

In this post we shall give another proof of the famous AM-GM-HM inequality: If are positive real numbers, then AM GM HM, precisely .

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Polynomial Optimization 2: SOS and SDP

In this article we shall describe something called Gram-matrix method which can decompose a polynomial into sum of squares. The notation means is a square symmetric positive semidefinite matrix.  Proposition 1.          Let , be a polynomial … Continue reading