This work deals with the study of structured backward error analysis of Hankel and symmetric-Toeplitz matrix pencils. These structured matrix pencils belong to the class of symmetric matrix pencils with some additional properties that a symmetric matrix pencil does not have in general. The perturbation analysis of these two structures is discussed one by one to depict the additional properties explicitly. Present work shows the entrywise structured perturbation of matrix pencils in Frobenius norm such that the specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil. The framework used here maintains the sparsity in the perturbation of the above-structured matrix pencils. Further, the backward error results help for solving a variety of inverse eigenvalue problems.

这项工作涉及Hankel和对称Toeplitz矩阵铅笔的结构化后向误差分析的研究。这些结构化的矩阵笔属于对称矩阵笔的一类，具有对称矩阵笔通常不具备的一些其他属性。逐一讨论了这两种结构的扰动分析，以明确描述附加属性。当前的工作显示了Frobenius范数中矩阵铅笔的入门结构化扰动，使得指定的特征对成为精确的特征对适当干扰的矩阵铅笔的数量。此处使用的框架在上述结构的矩阵笔的扰动中保持稀疏性。此外，后向误差结果有助于解决各种反特征值问题。