Questions tagged [algorithms]

A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.

24
votes
6answers
4k views

How can the gravitational n-body problem be solved in parallel?

How can the gravitational n-body problem be solved numerically in parallel? Is precision-complexity tradeoff possible? How does precision influence the quality of the model?
43
votes
7answers
4k views

Is algorithmic analysis by flop-counting obsolete?

In my numerical analysis courses, I learned to analyze the efficiency of algorithms by counting the number of floating-point operations (flops) they require, relative to the size of the problem. For ...
18
votes
2answers
288 views

Is there an efficient algorithm for matrix-valued continued fractions?

Suppose I have a matrix equation recursively defined as A[n] = inverse([1 - b[n]A[n+1]]) * a[n] Then the equation for A[1] looks similar to a continued fraction,...
16
votes
3answers
256 views

Uses of power series maps

I'm from the field of accelerator physics, specifically related to circular storage rings for synchrotron light sources. High energy electrons circulate around the ring, guided by magnetic fields. ...
7
votes
1answer
1k views

Alternative to Bron-Kerbosch algorithm for enumerating maximal cliques in inverse interval graphs

I often use inverse interval graphs to represent biologically relevant features along a genomic sequence. For example, given a (relatively) small genomic region, the graph would contain a node for ...