On the Convergence of the Conjugate Residual Method for Singular Systems
-
- HAYAMI Ken
- Foundations of Informatics Research Division National Institute of Informatics
Bibliographic Information
- Other Title
-
- 特異な系に対する共役残差法の収束性について
- トクイ ナ ケイ ニ タイスル キョウヤク ザンサホウ ノ シュウソクセイ ニ ツイテ
Search this article
Abstract
Consider applying the Conjugate Residual (CR) method to systems of linear equations Ax = b or least squares problems min__<x∈R^2>‖b-Ax‖_2, where A ∈ R^<n×n> is singular and nonsymmetric. First, we prove that the necessary and sufficient condition for the method to converge to a least squares solution without breaking down for arbitrary b and initial approximate solution x_0 is that the symmetric part M(A) of A is semi-definite, rank M(A) = rankA, and R(A)^⊥ = kerA. Next, we derive the necessary and sufficient condition for the CR method to converge to a solution without breaking down for arbitrary b ∈ R(A) and arbitrary x_0.
Journal
-
- Transactions of the Japan Society for Industrial and Applied Mathematics
-
Transactions of the Japan Society for Industrial and Applied Mathematics 13 (1), 1-33, 2003
The Japan Society for Industrial and Applied Mathematics
- Tweet
Details 詳細情報について
-
- CRID
- 1390001205768082560
-
- NII Article ID
- 110001878206
-
- NII Book ID
- AN10367166
-
- ISSN
- 09172246
- 24240982
-
- NDL BIB ID
- 6514355
-
- Text Lang
- ja
-
- Data Source
-
- JaLC
- NDL
- CiNii Articles
- KAKEN
-
- Abstract License Flag
- Disallowed