论文标题
伪对称矩阵的结构保存划分和诱导方法
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices
论文作者
论文摘要
我们为矩阵设计了一个频谱划分和诱导方案，这些矩阵与给定的不确定标量产物（即假性矩阵）相对于自动化。基质的假对称结构保留在光谱划分中，以便可以递归地应用该方法以实现完全对角线化。该方法非常适合在计算量子物理和化学中出现的结构化矩阵。在此应用程序上下文中，当使用Zolotarev函数时，在两个步骤内保证了矩阵符号函数迭代的收敛性。这些步骤很容易平行。此外，显示矩阵将光谱划分仅一步之后，将矩阵分解为对称的确定特征值问题。
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division, such that the method can be applied recursively to achieve full diagonalization. The method is well-suited for structured matrices that come up in computational quantum physics and chemistry. In this application context, additional definiteness properties guarantee a convergence of the matrix sign function iteration within two steps when Zolotarev functions are used. The steps are easily parallelizable. Furthermore, it is shown that the matrix decouples into symmetric definite eigenvalue problems after just one step of spectral division.
