论文标题
hermitian $ j $ - 对称特征值问题的厚实的兰有类型方法
A thick-restart Lanczos type method for Hermitian $J$-symmetric eigenvalue problems
论文作者
论文摘要
为Hermitian $ j $ -smmetric矩阵提出了一种厚实的兰有型算法。由于Hermitian $ J $ - 对称矩阵具有双重变性或双重多个特征值，并且在退化的特征向量之间具有简单的关系，因此我们可以通过限制lanczos algorithm的融合来限制Krylov seach sekspace space spainter of newemeneper of nemeal eylease paireneper pereene peremen eylease pereene pairs eyeles eyeles eyeles eyement a。我们可以提高其融合。我们表明，兰开斯迭代与$ j $ -symmetry兼容，因此可以将子空间分成两个彼此正交的子空间。所提出的算法在没有多重性的情况下搜索两个子空间之一中的特征向量。与$ j $ -smmetry的简单关系可以轻松地重建与它们配对的其他特征向量。我们在随机生成的小密集矩阵和稀疏的大矩阵上测试算法，该基质源自量子场理论。
A thick-restart Lanczos type algorithm is proposed for Hermitian $J$-symmetric matrices. Since Hermitian $J$-symmetric matrices possess doubly degenerate spectra or doubly multiple eigenvalues with a simple relation between the degenerate eigenvectors, we can improve the convergence of the Lanczos algorithm by restricting the search space of the Krylov subspace to that spanned by one of each pair of the degenerate eigenvector pairs. We show that the Lanczos iteration is compatible with the $J$-symmetry, so that the subspace can be split into two subspaces that are orthogonal to each other. The proposed algorithm searches for eigenvectors in one of the two subspaces without the multiplicity. The other eigenvectors paired to them can be easily reconstructed with the simple relation from the $J$-symmetry. We test our algorithm on randomly generated small dense matrices and a sparse large matrix originating from a quantum field theory.
