This post has published on my own website: https://brainbomb.org/0-introduction-to-numerical-analysis-blogs/
Hi everyone, I’m Tony. This is my first blog in this new website where contains knowledge all about Artificial Intelligence, such as mathematics, program design, algorithm, and so on.
This series is about ‘Numerical Analysis’, and I use the book written by Timothy Sauer, named ‘Numerical Analysis’.
AI or such sort of subjects have been solving problems by computers, and what we do every day is that: firstly, we translate real-world problems into mathematical problems, and then we tell the computers what they should do, and this process is called ‘programming’ as well. Though you may be the same position as me where our duty is to design algorithms, which exactly is the first step, the head, on the chain. It’s exciting and necessary for every algorithm designer to verify their algorithms. However, we can never verify our algorithms without computation on a computer.
Through this subject, numerical analysis, we are going to make a close study of computations done by modern computers. And we will see the details of machine arithmetic and how a poor-designed calculation ruin the whole project.
Introduction to Chapter 0
In this chapter, we will discuss:
1. Efficient methods for evaluating polynomials
2. Binary number system
3. The effects of the small rounding errors on computations
The most fundamental operations of arithmetic are addition and multiplication. When I read ‘Real Analysis’[Tao, 2006], Prof. Tao builds the first numerical system by defining nature numbers(1,2,3,4…) and then addition and multiplication. We should pay more attention to the most fundamental operations, for the more basic operation is, the more we stand to gain by doing it right. And on the other hand, the more basic operation is, the more times they will be used in our further work.
My English blog career begins from this day, and I’m trying my best to be an AI scientist, which is my whole life dream, even though I have wasted 28 years of my life. And you are welcome to leave me a message or mail me for everything.
- Tao T. Analysis[M]. Hindustan Book Agency, 2006.