Backward error analysis and inverse eigenvalue problems for Hankel and Symmetric-Toeplitz structures

Highlights：

• Backward error analysis of one or more specied eigenpairs for Hankel and symmetricToeplitz matrices/ matrix pencils is discussed in detail.

• For both the structures, minimum norm perturbed matrix pencils are obtained such that given eigenpairs become exact, which also preserve the sparsity.

• Backward error results are developed using Frobenius norm.

• Inverse eigenvalue problems and generalized inverse eigenvalue problems are solved for Hankel and symmetric-Toeplitz structures.

• Solutions of inverse eigenvalue problems using backward error analysis show that backward error analysis and inverse eigenvalue problems are interconnected.

摘要

•Backward error analysis of one or more specied eigenpairs for Hankel and symmetricToeplitz matrices/ matrix pencils is discussed in detail.•For both the structures, minimum norm perturbed matrix pencils are obtained such that given eigenpairs become exact, which also preserve the sparsity.•Backward error results are developed using Frobenius norm.•Inverse eigenvalue problems and generalized inverse eigenvalue problems are solved for Hankel and symmetric-Toeplitz structures.•Solutions of inverse eigenvalue problems using backward error analysis show that backward error analysis and inverse eigenvalue problems are interconnected.

论文关键词：Matrix pencil,Backward error,Hankel generalized eigenvalue problems,Symmetric-Toeplitz generalized eigenvalue problem,Generalized inverse eigenvalue problem

论文评审过程：Received 10 April 2020, Revised 4 February 2021, Accepted 11 April 2021, Available online 7 May 2021, Version of Record 7 May 2021.