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.
The purpose of this lecture is to understand the derivations and algorithms of various numerical solution methods, and to
be able to apply them to real problems through implementation.
- Implement the Lagrange interpolation method and perform interpolation for given data.
- Understand the working principle of spline interpolation method, implement it on a computer, and perform interpolation for given data.
- Understand the derivation and operating principles of algorithms for eigenvalue problems, and be able to compute eigenvalues in practice.
- Understand the derivation of numerical methods for solving least squares problems and be able to solve them.
- Understand the principle of operation of the conjugate gradient method and be able to calculate approximate solutions on a computer.
| 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, QR decomposition | Review of previous classes | 190minutes |
| 9. | Matrix factorization 2: 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. | PC exercises | Review of previous classes | 190minutes |
| Total. | - | - | 2660minutes |
| report | assignment | Total. | |
|---|---|---|---|
| 1. | 20% | 5% | 25% |
| 2. | 20% | 5% | 25% |
| 3. | 20% | 10% | 30% |
| 4. | 20% | 20% | |
| Total. | 80% | 20% | - |
Textbooks will not be specified; materials will be distributed as needed.
- Office hours: Tuesday, 4th period
Questions will be accepted via email, zoom (please email in advance), chat, etc.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic self-management skills
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
Last modified : Sat Mar 19 04:41:14 JST 2022