# Tag Info

### Good examples of "two is easy, three is hard" in computational sciences

One example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two-body problem. The two-body problem here means the task of calculating the ...

### Good examples of "two is easy, three is hard" in computational sciences

In one and two dimensions, all roads lead to Rome, but not in three dimensions. Specifically, given a random walk (equally likely to move in any direction) on the integers in one or two dimensions, ...

### Good examples of "two is easy, three is hard" in computational sciences

A famous example is the boolean satisfiability problem (SAT). 2-SAT is not complicated to solve in polynomial time, but 3-SAT is NP-complete.

### Good examples of "two is easy, three is hard" in computational sciences

In social choice theory, designing an election scheme with two candidates is easy (majority rules), but designing an election scheme with three or more candidates necessarily involves making trade-...

### Good examples of "two is easy, three is hard" in computational sciences

Here's one close to the hearts of the contributors at SciComp.SE: The Navier–Stokes existence and smoothness problem The three-dimensional version is of course a famous open problem and the subject ...
Accepted

### How do I find the minimum-area ellipse that encloses a set of points?

Theory The 1997 paper "Smallest Enclosing Ellipses -- Fast and Exact" by Gärtner and Schönherr addresses this question. The same authors provide a C++ implementation in their 1998 paper &...

### Good examples of "two is easy, three is hard" in computational sciences

Simultaneous diagonalization of two matrices $A_1$ and $A_2$: $$U_1^T A_1 V = \Sigma_1,\quad U_2^TA_2V=\Sigma_2$$ is covered by existing generalized singular value decomposition. However, when the ...

Accepted

### Rank constrained SDP

The constraint $\mbox{rank}(X) <= d$ is in general a non-convex constraint. Sorry. A commonly used approach is to minimize the Schatten 1-norm of X (the sum of singular values of X) as a ...
If your element is quadratic, you can find an implicit equation of the three quadratic edges of the triangle in function of $x,y$, in the form $E_1(x,y)=0$, $E_2(x,y)=0$, $E_3(x,y)=0$ (more ...