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      Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications

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          Abstract

          We present a novel algorithm to perform the Hessenberg reduction of an \(n\times n\) matrix \(A\) of the form \(A = D + UV^*\) where \(D\) is diagonal with real entries and \(U\) and \(V\) are \(n\times k\) matrices with \(k\le n\). The algorithm has a cost of \(O(n^2k)\) arithmetic operations and is based on the quasiseparable matrix technology. Applications are shown to solving polynomial eigenvalue problems and some numerical experiments are reported in order to analyze the stability of the approach

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          The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order

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            Solving polynomial eigenvalue problems by means of the Ehrlich–Aberth method

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              An implicitQR algorithm for symmetric semiseparable matrices

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                Author and article information

                Journal
                10.1016/j.laa.2015.08.026
                1501.07812

                Numerical & Computational mathematics
                Numerical & Computational mathematics

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