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Numerical Analysis

Hi everyone, This is my first blog in this new website where contains knowledge all about Artificial Intelligence, such as mathematics, program design, algorithms, 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 for a long time, and what we do every day is always like that: firstly, we translate real-world problems into mathematical problems(we might call this mathematical model), and then we tell the computers what they should do, which is called ‘programming’ as well. Though you may be in the same position as mine where our duty is to design algorithms, which exactly is the first step. It’s exciting and necessary for every algorithm designer to verify their algorithms. However, we can never make it without the help of a computer.
Through this subject, numerical analysis, we are going to make a close look at computations done by modern computers. And we will see the details of machine arithmetic and how a poor-designed calculation ruin the whole project.

What we will learn

In chapter 0

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 take in our further work.

Conclusion

My English blog career begins from this day, and I’m trying my best to be an AI scientist, which is my lifelong pursuit, even though I have wasted 28 years of my life. And you are welcome to leave me a message or mail me for everything.

Reference

  1. Tao T. Analysis[M]. Hindustan Book Agency, 2006.