Abstract
The main result of the present paper is a method to transform a matrix or operator which has a hierarchical semi-separable (HSS) representation into a URV (Moore-Penrose) representation in which the operators U and V represent collections of efficient orthogonal transformations and the block upper matrix R still has the HSS form. The paper starts with an introduction to HSS-forms and a survey of a recently derived multi resolution representation for such systems. It then embarks on the derivation of the main ingredients needed for a Moore-Penrose reduction of the system while keeping the HSS structure. The final result is presented as a sequence of efficient algorithmic steps, the efficiency resulting from the HSS structure that is preserved throughout.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Dewilde, P., Chandrasekaran, S. (2006). A Hierarchical Semi-separable Moore-Penrose Equation Solver. In: Alpay, D., Luger, A., Woracek, H. (eds) Wavelets, Multiscale Systems and Hypercomplex Analysis. Operator Theory: Advances and Applications, vol 167. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7588-4_3
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DOI: https://doi.org/10.1007/3-7643-7588-4_3
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