论文标题
更新结构化矩阵铅笔，对未衡量的光谱数据没有溢出效应和放气对
Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair
论文作者
论文摘要
本文致力于研究基质铅笔（结构化或非结构化）的扰动，因此扰动的铅笔将重现给定的放气对，同时保持互补的缩水对的不变性。如果后者未知，则称为无溢更新。本文中考虑的特定结构包括对称，Hermitian，$ \ star $ -EVIN，$ \ star $ -odd和$ \ star $ -skew-skew-hamiltonian/hamiltonian铅笔。这项研究是由众所周知的有限元模型更新问题中的结构动力学中的动机，其中给定的放气对代表一组给定的本本植物，互补的放气对表示剩余的较大的特征材料集。结构保存的分析表达式未确定用于放气结构化基质铅笔对的溢出更新。此外，当已知给定的非结构化铅笔的互补放气对时，将获得所有可能的非结构化扰动的参数表示。此外，获得参数表达式用于结构化更新，并具有某些理想的结构，这些结构与对称阳性定期或半明确矩阵铅笔的现有结果有关。
This paper is devoted to the study of perturbations of a matrix pencil, structured or unstructured, such that a perturbed pencil will reproduce a given deflating pair while maintaining the invariance of the complementary deflating pair. If the latter is unknown, it is referred to as no spillover updating. The specific structures considered in this paper include symmetric, Hermitian, $\star$-even, $\star$-odd and $\star$-skew-Hamiltonian/Hamiltonian pencils. This study is motivated by the well-known Finite Element Model Updating Problem in structural dynamics, where the given deflating pair represents a set of given eigenpairs and the complementary deflating pair represents the remaining larger set of eigenpairs. Analytical expressions of structure preserving no spillover updating are determined for deflating pairs of structured matrix pencils. Besides, parametric representations of all possible unstructured perturbations are obtained when the complementary deflating pair of a given unstructured pencil is known. In addition, parametric expressions are obtained for structured updating with certain desirable structures which relate to existing results on structure preservation of a symmetric positive definite or semi definite matrix pencil.
