So after studying the Runge-Kutta method, I looked around the web to see what these guys were about (and how to pronounce it).  Here is the pronunciation for all those who were wondering:(roon-ge cut-ah)  It turns out they are both german mathematicians rocking (or at least in some pictures) some serious mustaches.  Behind the staches […]

Monte Carlo methods require a series of random numbers. The most straightforward way to obtain these numbers is to use the rand() function in Matlab or a similar function in a different software system. These numbers are, of course, only pseudo-random – they are generated by an algorithm and no actual chance is […]

 
Towards the end of our class, we have been paying attention to Monte Carlo techniques. Monte Carlo simulation, which randomly generates values for uncertain variables over and over to simulate a model, have the advantage of factoring uncertainty into the processes where it is applied. Stanislow Ulam might be amused to learn that his Monte […]

Humanity’s taming of fire was supposedly one of the defining moments in early human history. Ever since, people have retained their fascination with fire. People may not regularly use fire nowadays for heat or light but they still love it anyway. Why else would there be so much research on modeling it? Well, some models […]

So apparently there’s a way to combine Prof James two favorite things: Graphics and really torturous numerical problems. In a full global illumination setting, where indirect lighting (light that bounces of a surface and lights another) is also computed, the goal of a renderer is to solve the rendering equation:

which is computing an integral over […]

While scanning through some papers about the Runge-Kutta method, I stumbled upon a 1993 paper entitled “The search for the Holy Grail, Or: Predictor-corrector methods for solving ODEIVPs,” written by Kevin Burrage, a professor of Computational Mathematics at the University of Queensland in Australia.  Sure, it’s pushing 15 years old now, but with a title […]

As we have seen in class, monte carlo methods of estimating things converge rather slowly. So, to get a relatively accruate result, we must use many many data points. Such a way of calculating desired results often requires supercomputers.
however, I found a paper on how to use Grid-computing to help solve some of this problem. […]

Over the past several years, airport and transportation security has become a major issue in the US and around the world.  The problem is that there are so many different scenarios for what could go wrong, why and how, that it’s unrealistic for security officials to reason about all the variables at play and […]

As many of my classmates have posted, the Monte Carlo method isn’t actually any single method, but actually represents an entire class of methods which involve taking random samples to find a result.  An interesting application my partner and I found for the Monte Carlo method was for one of the GO AIs we made for one of our other projects. […]

As we’ve seen in class and in our textbook, the estimation of Pi through Monte Carlo simulations is a pretty casual and standard example.  It’s a good one too since it allows us to visualize the norms of setting up a Monte Carlo simulation, and see what the method actually achieves.  The Monte Carlo method […]