The earliest known mention of matrices to solve systems of linear equations occurred in Jiuzhang suanshu or Nine Chapters on the Mathematical Art, a Chinese mathematical treatise from 100 to 200 BC. The treatise not only describe the process of Naive Gaussian Elimination to solve linear equations but also introduces the concept of a […]

The first project of this class was about a small part of ray tracing. Here is a description of another method used for ray tracing, a recursive algorithm.
The basic idea is identical in the root finding project: shoot a ray, find the first one instance intersecting with the light. And it finds all the objects […]

 http://ieeexplore.ieee.org/iel5/7192/19378/00895395.pdf
One of the main difficulties with using fingerprints (as evidence, record-keeping, etc) is that there are many factors that make sampling someone’s fingerprint inherently inaccurate (e.g. low quality scanning technology, issues with skin itself, etc). Thus a good fingerprint image-enhancing algorithm is something that would be very useful in this day and age. Until recently, […]

You’re probably wondering what this gif has to do with least-squares, or CS 322 in general. Well, it is actually a demonstration of some of Dr. James’s research (along with Alec Rivers), into the deformation of objects, and guess what, the underlying algorithm does in fact use a least squares approximation to get those […]

Alcohol Breath Testing and Least Squares Data Fitting
The above link is to a study at North Carolina State University investigating the mathematics behind how breathalyser tests calculate a persons Blood Alcohol Content (BAC). It turns out (not surprisingly) that if a person takes several breathalyser tests one after another, their results can vary […]

Who ever thought that something you learned in class would actually be useful to you on a Saturday night when you wanted to just relax and kick back with some friends and your favorite bottle of scotch whiskey?  Well, the authors of this article, “Clustering of Scotch Whiskeys using Non-Negative Matrix Factorizations” from the SPES/Q&P […]

DNA Computing is a rising interdisciplinary field, that uses the four DNA bases (A, T, C, G) to perform computation. It attempts to exploit the relationships between the base pairs to create faster, in some situation, computational machines. The field was created by Leonard Adleman in 1994. He demonstrated it was possible […]

Many of you know what the butterfly effect is and and have seen the movie with that same title, but its doubtful whether many people know the origins of the name. The butterfly effect is the idea that a single flap of a butterfly’s wings could have large scale effects across the world. […]

Working on the projects, you must have had complained about the long running time of your Matlab code when you do a computation on huge matrices. Why do larger matrices take much longer running time? One of the obvious reasons is because there are more numbers to calculate with. If you are a very […]

Non-matrix factorization has many applications.  One of them aforementioned is in facial recognition.  There are several applications in medicine.  One technique called CGH or comparative genomic hybridization has been used to analyze samples from patients with myeloma and has aided in the identifications of four genetic subtype.  This was done using a algorithm using non-negative […]