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A Galerkin Approach for Solving Matrix Equations with Hierarchical Matrices
Author(s) -
Boysen Dirk,
Börm Steffen
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310198
Subject(s) - matrix (chemical analysis) , space (punctuation) , mathematics , galerkin method , sparse matrix , algebra over a field , product (mathematics) , iterative method , mathematical optimization , computer science , pure mathematics , physics , nonlinear system , geometry , materials science , gaussian , operating system , quantum mechanics , composite material
We consider a new approach for computing solutions of certain matrix equations, for example AXA = C , AX + XB = C or AX = I . This approach is based on a variational formulation in the matrix space, employing the Frobenius inner product. Using the space of ℋ 2 ‐matrices as trial space leads to a sparse linear system that can be solved by iterative methods to compute an approximate solution of the underlying matrix equation. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)