Lots of numerical methods have parameters (i.e. tolerance, momentum …). While we would want to optimize the parameters and not use the default values (i.e. in 322 project), it is often very difficult to optimize them.
In general, what people do is prepare a test set, run your numerical methods with different parameter values, […]

With so many hot applications like computer graphics, advanced audio synthesis, and video relying heavily on matrix multiplication, Apple is making efforts to make this process more efficient and accurate with a dedicated vector processing unit (VPU) that can be carried out these operations for various applications.  Rather than having to simplify the […]

There are many ways to compute the n-th Fibonacci number easily: there is a well-known close formula. Another approach is matrix multiplication.
Let’s take a look at this approach first.
As we all know, Fk+2 = Fk+1 + Fk. Thus, we can expand this equation to a matrix equation:
[1]
Now, it’s easy to see the following:
[2]
Now, […]

Throughout this course we’ve run into many examples of the peculiarities of doing mathematical calculations on computers: catastrophic subtraction, nested multiplication for efficient computation of polynomial sums, being unable to represent numbers smaller than machine precision, etc are just a few of the issues brought up in class.
Much of this stems from the fact that […]

“NUMBERS of the form nsqrt{-1} are imaginary, but can still be used in equations.”[1]
After seeing this, I was really stunned at what in the world that equation means.
Later, I found another weird equations through xkcd #217[2].
I was really confused and I decided to find out what these equations mean and/or how they can be computed, […]

For our first project we have used ray tracing to create images of objects. As a result we were able to get decent images of long extinct water(?) bunnies. However, aside from the root calculation, tracing an object took a long time. It was obvious that once the images became complex, ray tracing would take […]

We have looked at truncation and rounding errors in class concerning the calculation of the first derivative. Such errors can be the nascent of major miscalculations when dealing with multi-step algorithms. Sinusoidal oscillators are one application where truncation and rounding errors can sway the result from the desired output. However, techniques such as interpolation come […]

Helen, a very clever girl, never makes any mistake on her homework. Her GPA used to be 4.3 until she got one miserable A due to a silly numerical computing error… it was a disaster.. a nightmare.. even now, she sometimes gets pissed off when she thinks about it. So, what happened to Helen last […]

Here’s a post to get this blog started.
In class we’ve been talking about root finding schemes such as the Bisection method, Newton’s method, etc., and how they can be used to evaluate functions such as sqrt(), invSqrt(), etc. That’s fine, but what would you use if you wanted a really fast implementation of […]

Welcome to the course blog for CS 322 “Introduction to Scientific Computing!” This course covers a wide variety of scientific computing concepts and numerical methods, and, through this blog, we will establish some of their connections to the real world. Topics should be interesting and related to numerical computing in some way. Posts […]