Newton's method

May 1, 2012 blog math

To numerically find a root of \(f(x)=0\), we may use the Newton’s method. Assuming the root is at the proximity of \(x_k\), to find a better approximate \(x_{k+1}\), we consider the tangent line at \((x_k, f(x_k))\), which is provided by the equation [more]

Solving Steiner Tree Problem as a MILP

April 10, 2012 blog math

Consider a network \(G(V,E)\), with \(W_0 \subset V\) is a set of focus vertices. Let’s call \(s\in W_0\) the multicast sender and the rest \(W = W_0 \backslash \{s\}\) the multicast receivers. Given the edges of unit weight, how to find the multicast tree that connects \(s\) to \(W\) with... [more]