Fast verified solutions of linear systems
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- 作者：Takeshi Ogita (12) ogita@lab.twcu.ac.jp
Shin鈥檌chi Oishi (3) oishi@waseda.jp - 关键词：Key words verified numerical computation ; verified solutions of linear systems ; self ; validating methods
- 刊名：Japan Journal of Industrial and Applied Mathematics
- 出版时间：October 2009
- 出版年：2009
- 期刊代码：141_1868-937X
- 类别：mat
- 卷：26
- 期：2-3
- 页码：169-190
- 数据来源：sp
摘要
This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear systems. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.