Apr, 2016 - Mar, 2019
Development of accurate algorithms for numerical linear algebra
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) Grant-in-Aid for Scientific Research (B)
- Grant number
- 16H03917
- Japan Grant Number (JGN)
- JP16H03917
- Grant amount
-
- (Total)
- 18,330,000 Japanese Yen
- (Direct funding)
- 14,100,000 Japanese Yen
- (Indirect funding)
- 4,230,000 Japanese Yen
For linear systems, we conducted on numerical algorithms that can always obtain the best approximate solution regardless of the condition number of the coefficient matrix.
We developed an iterative improvement algorithm for eigenvectors with quadratic convergence for symmetric eigenvalue problems. This enables us to develop a numerical algorithm that can always obtain the best approximate solution. We also developed a numerical algorithm that can always obtain the best approximate solution of singular value problems for nonsymmetric matrices.
In order to improve the efficiency of the above proposed algorithms, we developed accurate matrix multiplication algorithms. In addition, as test problems in numerical linear algebra, we developed methods for generating problems with exact solutions.
We developed an iterative improvement algorithm for eigenvectors with quadratic convergence for symmetric eigenvalue problems. This enables us to develop a numerical algorithm that can always obtain the best approximate solution. We also developed a numerical algorithm that can always obtain the best approximate solution of singular value problems for nonsymmetric matrices.
In order to improve the efficiency of the above proposed algorithms, we developed accurate matrix multiplication algorithms. In addition, as test problems in numerical linear algebra, we developed methods for generating problems with exact solutions.
- Link information
- ID information
-
- Grant number : 16H03917
- Japan Grant Number (JGN) : JP16H03917