matrix multiplication within PHP?
frisco: From my experience, numerical algorithms at all complicated in PHP tend to lead to major suckage.  We use Thrift (http://incubator.apache.org/thrift/) to send the task to a daemon written in something more reasonable, most often either Python or C depending on required intensity.  Works beautifully, few problems.  Also, this lets you run the task asynchronously, so you can still return the page in N ms and then load the results on a lag: responsivity means a huge amount to users.  Nothing's worse than the script dying from memory limits or timeouts and having the user get nothing (and PHP doesn't do threading).