Course title
V04259002
Numerical Analysis 2

 FUKUDA Akiko Click to show questionnaire result at 2019
Course description
Numerical analysis and numerical algorithms, which are the fundamental technologies of numerical simulation, have become indispensable technologies in today's research and development due to the recent development of computer environments. The performance of computers has been remarkably improved, and various tools running on them have been enriched, creating an environment in which simulations can be performed easily. However, if we lack understanding of the fundamental principles of any tool, we may sometimes misuse it and make a big mistake. This course is a continuation of Numerical Analysis I. The purpose of this course is to teach the basics of interpolation methods, eigenvalue problems, least-squares problems, etc., as well as numerical calculation methods and algorithms, and to equip students with the skills to perform appropriate numerical calculations and evaluate results correctly. The class will consist mainly of lectures, but students will also learn to program and perform numerical experiments using computers.
Purpose of class
The purpose of this lecture is to understand the derivations and algorithms of various numerical methods, and to be able to apply them to real problems through implementation.
Goals and objectives
  1. Understand the working principle, implement the interpolation method and perform interpolation for given data.
  2. Understand the derivation and operating principles of algorithms for eigenvalue problems, and be able to compute eigenvalues in practice.
  3. Understand the derivation of numerical methods for solving least squares problems and be able to solve them.
  4. Understand the principle of operation of the conjugate gradient method and be able to calculate approximate solutions on a computer.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 report final exam Total.
1. 10% 15% 25%
2. 10% 15% 25%
3. 10% 15% 25%
4. 10% 15% 25%
Total. 40% 60% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance
Interpolation Method 1: Lagrangian interpolation 		Review of Numerical Analysis I 190minutes
2. Interpolation Method 2: Newton Interpolation Review of previous classes 190minutes
3. Interpolation Method 3: PC Exercise Review of previous classes 190minutes
4. Interpolation Method 4: Spline Interpolation (1) Review of previous classes 190minutes
5. Interpolation Method 5: Spline Interpolation (2) Review of previous classes 190minutes
6. Interpolation Method 6: PC Exercise Review of previous classes 190minutes
7. Eigenvalue problem: Power method Review of previous classes 190minutes
8. Matrix factorization 1: Cholesky decomposition and its application to eigenvalue problems Review of previous classes 190minutes
9. Matrix factorization 2: QR decomposition and its application to eigenvalue problems Review of previous classes 190minutes
10. Least squares problem: Normal equations Review of previous classes 190minutes
11. Least squares problem: A method using matrix factorization Review of previous classes 190minutes
12. Conjugate gradient method 1: Minimizing residuals Review of previous classes 190minutes
13. Conjugate gradient method 2: Krylov subspace Review of previous classes 190minutes
14. Review and final exam Review of previous classes 190minutes
Total. - - 2660minutes
Evaluation method and criteria
Final examination (60%), report (40%)
A pass is awarded if the student understands the derivation of each numerical method, implements it on a computer and actually performs numerical experiments, and makes an appropriate evaluation of the results obtained.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Textbooks will not be specified; materials will be distributed as needed.
Prerequisites
None
Office hours and How to contact professors for questions
  • Office hours: Tuesday, lunch time
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic self-management skills
  • Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Tue Feb 20 04:06:41 JST 2024