Finding the closest normal structured matrix

Abstract

Given a structured matrix $A$ we study the problem of finding the closest normal matrix with the same structure. The structures of our interest are: Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop a structure-preserving Jacobi-type algorithm for finding the closest normal structured matrix and show that such algorithm converges to a stationary point of the objective function.

arXiv commentSubmission arXiv:1810.03369v1 [math.NA] is split into two parts. This is a part dealing with the problem of finding the closest normal matrix. 24 pages, 4 figures, 1 table

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