Spectral Dichotomy of a Matrix Pencil with Respect to a Circle, Ellipse or Parabola not Centered at the Origin

Spectral dichotomy methods of a matrix pencil which calculate projectors on the subspace associated with the eigenvalues inside or outside of any circle, any ellipse or any parabola, were proposed. These methods are an extension of those proposed in [S. Traoré and M. Dosso, European Journal of Pure and Applied Mathematics, 15(2), (2022)681-725] and [S. Traoré, M. Dosso and L Samassi, International Journal of Numerical Methods and Applications, 22, (2022) 87-115] to matrix pencil. Before the presentation of our methods, a reminder of the spectral dichotomy methods of a matrix with respect to any circle, any ellipse or any parabol was made. Two numerical examples of matrix pencil show the good calculation of the projectors on the subspaces associated with the part of the plane concerned by the separation made by the gures.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.