Improving the Accuracy of Computed Matrix Eigenvalues
Improving the Accuracy of Computed Matrix Eigenvalues
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DOI：
10.2172/5047973
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发表时间：
1980-08
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影响因子：
--
通讯作者：
J. Dongarra
中科院分区：
文献类型：
--
作者：
J. Dongarra
描述了一种提高给定特征值及其相关特征向量的精度的计算方法，该特征值及其关联的特征向量是通过较低精度的计算得到的。将要描述的方法将增加配对的精度，并且以相对较低的成本这样做。所使用的技术类似于求解线性系统的迭代求精；即通过从低精度计算中进行因式分解，应用迭代算法来提高特征对的精度。该算法在临界点采用扩展精度算法。迭代算法每次迭代需要O(n？)次运算。
A computational method is described for improving the accuracy of a given eigenvalue and its associated eigenvector, arrived at through a computation in a lower precision. The method to be described will increase the accuracy of the pair and do so at a relatively low cost. The technique used is similar to iterative refinement for the solution of a linear system; that is, through the factorization from the low-precision computation, an iterative algorithm is applied to increase the accuracy of the eigenpair. Extended precision arithmetic is used at critical points in the algorithm. The iterative algorithm requires O(n²) operations for each iteration.