A Hierarchical Semi-separable Moore-Penrose Equation Solver
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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.
KeywordsHierarchically semi-separable systems hierarchically quasi-separable systems Moore-Penrose inverse structured matrices
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