There are many instances in which the financial world utilizes scientific computing.  In many cases, numbers need to be crunched.  However, there are times when calculations would be very tough that computers cannot perform them in a reasonable amount of time.  As we have learned, there are many ways to simplify the calculations (through nested […]

Usually, when we think of supercomputers, we think of large, precision-cooled rooms lined with large machines. But one the most powerful such systems is a distributed system known as Folding@Home, led by the researchers in the Department of Chemistry at Stanford University. This system was the first computer system to reach 1 petaflop (10^15 floating […]

We often discuss the practical applications of scientific computing and numerical analysis—how to solve complex mathematical systems with some arbitrary precision or how to perform some statistical analysis from a set of real-world data while minimizing error. Sometimes, however, it’s just cool to use these complex ideas to make pretty pictures. Science News […]

For those who don’t keep up with the gaming world, Team Fortress 2 is the latest first person shooter multiplayer game produced by Valve Corporation. It has gotten positive reviews for many attributes such as balance and gameplay, but one thing that really makes it stand out from other shooter games is its unique […]

There have been many incidents where bad numerical computing practices have led to massive financial and structural losses. Poor handling of rounding errors led to the Patriot Missile failure in Dharan Saudi Arabia on February 25 1991, and an integer overflow led to the explosion of the Ariane rocket just after lift-off on its maiden […]

Real-time networked games are remarkably difficult to build well. The main challenge in designing these types of games is dealing with network lag. The term “real-time” implies that you want a remote player’s actions to be reflected on your own screen virtually instantaneously and accurately. This goal is hampered by the fact that it takes […]

Yet another method of interpolation is splines, of which B-splines, Cubic Hermite splines, and NURBS (non-uniform ration B-spline) are just a few of the options. In general, a spline is a smooth piecewise function interpolating between its control points, also called knots. In the case of NURBS, a spline is determined by weighting the […]

We have seen the idea of nested multiplication, which provides one answer to the question: “How do I evaluate this polynomial quickly?”.
One interesting related question is: “How do I multiply these two numbers quickly?”. Using normal elementary school multiplication we achieve a O(n²) runtime for multiplying two n-bit numbers together. I’ve come across an […]

We might not realize it, but everytime we use Adobe Photoshop, we’re actually using interpolation techniques. Think about it this way - what happens when we resize/rotate/enlarge a photograph? There are only so many pixels involved in the image, that we will need to infer the type of pixel that we will need to fill […]

Is Matrix Inversion really a N^3 process?
In class, we mentioned about Vandermonde Matrixs, and the difficulty of this matrix inversion. Is process of matrix inversion really a N^3? Let’s think about it with 2 by 2 matrix.
Suppose we want to have the matrix multiplication A * B = C:
[…]