Practical use of the symmetric Lanczos process with re-orthogonalization
Practical use of the symmetric Lanczos process with re-orthogonalization
复制标题
具有重新正交化的对称 Lanczos 过程的实际应用
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
C. Paige
中科院分区：
文献类型：
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作者：
C. Paige
大型对称矩阵的几个极端特征值和向量通常可以通过执行远少于Lanczos过程的全部步骤来找到机器精度。为了证明这些结果的准确性，在这里给出了重新正交化的过程的舍入误差分析。它被发现，停止标准已被引入，以获得先验误差界。
Several extreme eigenvalues and vectors of large symmetric matrices can often be found to machine accuracy by carrying out far less than the full number of steps of the Lanczos process. To prove the accuracy of such results a rounding error analysis of the process with re-orthogonalization is given here. It is found that a stopping criterion has to be introduced to obtain a priori error bounds.