Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization
Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization
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DOI：
10.1137/0718008
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发表时间：
1981-02
影响因子：
2.9
通讯作者：
D. Scott
中科院分区：
文献类型：
--
作者：
D. Scott
本文讨论了求广义特征值问题的代数最小(或最大)特征值的迭代技巧，其中A和M是实的，对称的，M是正定的。我们假设A和M使得矩阵$A-\sigma M$对于任何$\sigma$的值都是不可取的。我们证明了该算法是全局收敛的，并且收敛是渐近二次的。最后，我们讨论了算法中需要进行的修改，以使其在计算上可行。
In this paper we discuss an iterative technique for finding the algebraically smallest (or largest) eigenvalue of the generalized eigenvalue problem $A - \lambda M$, where A and M are real, symmetric, and M is positive definite. We assume that A and M are such that it is undesirable to factor the matrix $A - \sigma M$ for any value of $\sigma $. We prove that the algorithm is globally convergent, and that convergence is asymptotically quadratic. Finally, we discuss the modifications required in the algorithm to make it computationally feasible.