Structured Backward Errors and Pseudospectra of Structured Matrix Pencils

Structured backward perturbation analysis plays an important role in the accuracy assessment of computed eigenelements of structured eigenvalue problems. We undertake a detailed structured backward perturbation analysis of approximate eigenelements of linearly structured matrix pencils. The structures we consider include, for example, symmetric, skew-symmetric, Hermitian, skew-Hermitian, even, odd, palindromic, and Hamiltonian matrix pencils. We also analyze structured backward errors of approximate eigenvalues and structured pseudospectra of structured matrix pencils.

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