## Course Title : Exercise on Numerical Analysis

Code 90920 3rd year 1st term 2 Seminar Kenji Harada, Akihiro Sato, Kinji Kimura, Hidemi Fukuda,

### Course Description

The numerical approach with computers is useful when we solve several problems in informatics and applied mathematics. In this exercise, we will learn numerical methods through implementing computer codes, executing the programs, and interpreting results.

The students MUST submit all the reports for four subjects. The score of each subject is 25 and the grading will be done based on the total scores of reports.

### Course Goals

We will learn fundamental techniques for numerical analysis with computers. Specifically, we aim at obtaining the following four techniques. (1) Understanding algorithm for numerical analysis, (2) Coding techniques (3) Methodology of data analysis, and (4) writing ability.

### Course Topics

Theme Class number of times Description
Guidance 1 We will explain contents of exercises on numerical simulations and introduce staffs and teaching assistants. We will further explain how to use computers in the computer room and account.
How to write your report 1 We will study how to write an efficient report.
Monte Carlo method 7 We will study the basic of Monte Carlo method which is a statistical method for simulating complex systems.
(a) Principle of Monte Carlo Method,
(b) Metropolis algorithm.
Parallelization of conjugate gradient method 7 It is the aim of this term to learn the methods for solving the linear equations of sparse matrices and implement parallel computing codes of the methods.
(a) The conjugate gradient method for solving linear equations of sparse symmetric positive definite matrices,
(b) The BiCG method for solving linear equations of sparse non-symmetric matrices.
Numerical method for data analysis 6 We will study fundamental methods which we need in data analysis.
(a) Statistical hypothesis test,
(b) Regression analysis.
Nonlinear optimization 6 We will study important methods of nonlinear optimization in the finite-dimensional vector space.
(a) Steepest descent method,
(b) Newton method.
Check for students' understanding 2 Based on reports, we will take supplementary lessons to understand contents of this exercise.

### Textbook

Not in particular. hand out.

### Textbook(supplemental)

[1]「HANPUKUHO NO SURI」（Author:Masaaki Sugihara and Kazuo Murota，Iwanami）

### Prerequisite(s)

Under the UNIX operating system, students have to edit a file, code and test C programs, make reports and graphs, and print them.