Computing Interior Eigenvalues of Large Matrices

提出了一种计算大矩阵几个内部特征值的新方法。假定矩阵的大小和结构使得因式分解不可行。新方法与瑞利-里兹方法有关，它以最优的方式求出内部特征值。该技术可以应用于对称矩阵的Lanczos算法，以及对称和非对称矩阵的Davidson和GD方法。当每次迭代的成本增加时，所需的迭代次数减少了。新方法可以是一个很大的改进。必须对这些方法进行测试，并开发适当的实现。必须确定哪些类型的问题新方法比现有的方法更好。

A new technique for computing a few interior eigenvalues of a large matrix is proposd. It is assumed that the size and structure of the matrix make factorization impractical. The new technique is related to the Rayleigh-Ritz, it finds interior eigenvalues in an optimal way. The technique can be applied to the Lanczos algorithm for symmetric matrices and to the Davidson and GD methods for both symmetric and nonsymmetric matrices. While the cost per iteration increases, the number of iterations needed decreases. The new methods can be a great improvement. The methods must be tested and the proper implementations developed. It must be determined for what types of problems the new methods are better than current methods.