Abstract
Here we consider inversion methods for some classes of matrices and representations. In the first section we apply the idea used in Section §13.4 for a general case of matrices with quasiseparable representations with invertible diagonal entries. In the second section we discuss an inversion method for matrices with lower quasiseparable and upper semisiseparable representations, under some restrictions on generators. This method is based on the representation of the matrix as a sum of an invertible lower triangular matrix and a matrix of a small rank. The same results are obtained in the subsequent Chapter 16 via the system approach.
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© 2014 Springer Basel
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Eidelman, Y., Gohberg, I., Haimovici, I. (2014). The First Inversion Algorithms. In: Separable Type Representations of Matrices and Fast Algorithms. Operator Theory: Advances and Applications, vol 234. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0606-0_14
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DOI: https://doi.org/10.1007/978-3-0348-0606-0_14
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0605-3
Online ISBN: 978-3-0348-0606-0
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