Localized spectrum slicing

摘要: Given a sparse Hermitian matrix $A$ and real number $\mu$, we construct set of vectors, each approximately spanned only by eigenvectors corresponding to eigenvalues near $\mu$. This vectors spans the column space localized spectrum slicing (LSS) operator, is called an LSS basis set. The sparsity related decay properties Gaussian functions. We present divide-and-conquer strategy with controllable error purely algebraic process using submatrices $A$, can therefore be applied general matrices. leads projected matrices reduced sizes, which allows problems solved efficiently techniques linear algebra. As example, demonstrate that used solve interior eigenvalue for discretized second order partial differential operator in one-dimensional two-dimensional domains, as well pattern.