基于多分辨率矩阵分解的快速分层预处理本征求解器
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition
AI总结：
本文提出一种基于多分辨率运算压缩框架的迭代方法，用于高效计算稀疏对称正矩阵的大量左本征对，通过整合隐式重启Lanczos方法与多分辨率框架，提出扩展-细化迭代方案以提高计算效率。
摘要：
本文提出了一种新的迭代方法，用于在多分辨率运算压缩框架下分层计算稀疏对称正矩阵的相对大量左本征对。我们通过将多分辨率框架整合到隐式重启Lanczos方法中，利用每个分解组件的良好条件性。我们通过提出扩展-细化迭代方案实现这种结合，其内在思想是将目标谱分解成若干段，使得每段对应的本征问题良好条件。理论分析和数值示例也展示了该算法的效率和有效性。
英文摘要：
In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition components by integrating the multiresolution framework into the Implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
