Numerical computations on matrices, such as solving linear equations, eigenvalues, singular values, etc., are collectively
called linear computations.
Linear computation is a fundamental technique in scientific and technological computations such as computer simulations, and it plays a very important role.
In this lecture, several linear computation algorithms related to singular value decomposition are discussed from various angles, such as derivation of each numerical method, error analysis, and relationship among each method.
Computer implementations are also given, and we touch not only on the theoretical aspects of the numerical methods but also on their applications to large-scale real-world problems in engineering and other applied fields.
Linear computation is a fundamental technique in scientific and technological computations such as computer simulations, and it plays a very important role.
In this lecture, several linear computation algorithms related to singular value decomposition are discussed from various angles, such as derivation of each numerical method, error analysis, and relationship among each method.
Computer implementations are also given, and we touch not only on the theoretical aspects of the numerical methods but also on their applications to large-scale real-world problems in engineering and other applied fields.
Various large-scale linear computations are required for scientific and technological calculations.
The purpose of this lecture is to understand the current status of linear computation and to gain a multidimensional understanding of the theoretical and applied aspects of linear computation methods.
The purpose of this lecture is to understand the current status of linear computation and to gain a multidimensional understanding of the theoretical and applied aspects of linear computation methods.
- Understand the need for large-scale linear computation in scientific computing.
- Understand the definition of singular value decomposition and be able to calculate singular value decomposition manually.
- Can perform singular value decomposition on large matrices.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Linear Computation in Scientific Computing | Review of Linear Algebra | 190minutes |
| 2． | Definition of Singular Value Decomposition | Review of previous classes | 190minutes |
| 3． | Properties of singular values (1) | Review of previous classes | 180minutes |
| 4． | Properties of singular values (2) | Review of previous classes | 190minutes |
| 5． | Tridiagonalization by Householder transformation | Review of previous classes | 190minutes |
| 6． | Numerical solution for singular value computation (1) | Review of previous classes | 190minutes |
| 7． | Numerical solution for singular value computation (2) | Review of previous classes | 190minutes |
| 8． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 9． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 10． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 11． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 12． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 13． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| 14． | (ends at the 7th week, since this is 1 credit class) | (ends at the 7th week, since this is 1 credit class) | 0minutes |
| Total. | - | - | 1320minutes |
| Report | Total. | |
|---|---|---|
| 1. | 30% | 30% |
| 2. | 35% | 35% |
| 3. | 35% | 35% |
| Total. | 100% | - |
Students will be evaluated based on a brief report on each class and a final report at the end of the term.
Students will get a credit if they understand the definition and properties of singular value computation, implement algorithms for numerical computation, and be able to perform numerical computation on large matrices.
Students will get a credit if they understand the definition and properties of singular value computation, implement algorithms for numerical computation, and be able to perform numerical computation on large matrices.
Sufficient knowledge of linear algebra I/II, (applied) numerical analysis I/II, and programming is desirable.
- Tuesday 4th period.
If you wish to visit the laboratory, it is advisable to contact the laboratory in advance.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A |
Last modified : Sat Sep 09 05:49:17 JST 2023