Abstract
We study divide and conquer method to compute eigenstructure of matrices with quasiseparable representation. In order to find the eigenstructure of a large matrix A we divide the problem into two problems for smaller sized matrices A and ?? by using the quasiseparable representation of A. In the conquer step we show that to reconstruct the eigenstructure of A from those of B and C amounts to the study of the eigenstructure of a rational matrix function. For a Hermitian matrix A which is order one quasiseparable we completely solve the eigenproblem.
Mathematics Subject Classification (2000). Primary 15A18; Secondary 26C15.
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Eidelman, Y., Haimovici, I. (2012). Divide and Conquer Method for Eigenstructure of Quasiseparable Matrices Using Zeroes of Rational Matrix Functions. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_12
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DOI: https://doi.org/10.1007/978-3-0348-0221-5_12
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