Course title
6M009000
Advanced Numerical Linear Algebra

 fukuda akiko
Course content
The scope of this course is to comprehend the numerical linear algebra,
in particular, numerical methods for linear systems and eigenvalue/singular value problems.
Purpose of class
Large-scale linear computation is needed in scientific computing. The purpose of this course is to understand the necessity and multilateral understanding of the theoretical aspects and applied aspects of linear computation.
Goals and objectives
  1. to understand the for large-scale linear computation in scientific computing
  2. to understand the derivation for the subspace iteration method and its theoretical/numerical properties
  3. to understand the derivation for the Krylov subspace method and its theoretical/numerical properties
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Eigenvalue problem(1) Eigenvalues and singular values Read Syllabus 190minutes
2． Eigenvalue problem(2) Householder transformation Review 190minutes
3． Eigenvalue problem(3) QR method Review 190minutes
4． Eigenvalue problem(4) Cholesky LR method and its convergence Review 190minutes
5． Eigenvalue problem(5) Shifted Cholesky LR method and its convergence Review 190minutes
6． Eigenvalue problem(6) qd and dqds method Review 190minutes
7． Eigenvalue problem(7) Eigenvalue algorithms derived from the discrete integrable system Review 190minutes
8． Linear systems(1) Conjugate gradient method Review 190minutes
9． Linear systems(2) Minimization property Review 190minutes
10． Linear systems(3) Termination of the iteration Review 190minutes
11． Linear systems(4) Implementation Review 190minutes
12． Linear systems(5) Preconditioning Review 190minutes
13． Linear systems(6) CGNR method Review 190minutes
14． Linear systems(7) Bi-CG method Review 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Report Total.
1. 30% 30%
2. 40% 40%
3. 30% 30%
Total. 100% -
Evaluation method and criteria
report (100%)
Textbooks and reference materials
Textbook is not specified. We will introduce a reference book if necessary.
Prerequisites
linear algebra, numerical analysis, programming
Office hours and How to contact professors for questions
  • Fri. 15:00～16:40
Relation to the environment
Non-environment-related course
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 problem-solving skills
Active-learning course
More than one class is interactive
Last modified : Wed Oct 17 07:54:24 JST 2018