Fast Verification of Solutions for Sparse Monotone Matrix Equations
Fast Verification of Solutions for Sparse Monotone Matrix Equations
复制标题
稀疏单调矩阵方程解的快速验证
DOI：
10.1007/978-3-7091-6217-0_14
复制
发表时间：
2001
影响因子：
1
通讯作者：
Yasunori Ushiro
中科院分区：
文献类型：
--
作者：
T. Ogita;S. Oishi;Yasunori Ushiro
本文讨论了系数矩阵稀疏单调的线性方程组数值解的精度检验问题。快速算法计算线性系统数值解的验证误差界和系数矩阵的保证条件数。所提出的验证方法是基于迭代求解方法和舍入模式控制计算。数值结果也表明，验证的成本是小于计算的数值解。
This paper concerns the problem of verifying the accuracy of a numerical solution for linear systems with a coefficient matrix being sparse and monotone. Fast algorithms calculate a verified error bound for numerical solutions of the linear systems and a guaranteed condition number of the coefficient matrix. The proposed verification method is based on iterative solution methods and rounding mode controlled computations. Numerical results have also been presented for illustrating that a cost for verification is less than that for calculating a numerical solution.