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Low rank solution of data‐sparse Sylvester equations
Author(s) -
Baur U.
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.605
Subject(s) - sylvester equation , sylvester's law of inertia , sylvester matrix , mathematics , computation , rank (graph theory) , sign (mathematics) , matrix (chemical analysis) , sparse matrix , scale (ratio) , function (biology) , algorithm , algebra over a field , mathematical optimization , pure mathematics , mathematical analysis , combinatorics , symmetric matrix , eigenvalues and eigenvectors , physics , materials science , matrix polynomial , quantum mechanics , polynomial matrix , evolutionary biology , biology , polynomial , composite material , gaussian
In this paper, a method for solving large‐scale Sylvester equations is presented. The method is based on the sign function iteration and is particularly effective for Sylvester equations with factorized right‐hand side. In this case, the solution will be computed in factored form as it is for instance required in model reduction. The hierarchical matrix format and the corresponding formatted arithmetic are integrated in the iteration scheme to make the method feasible for large‐scale computations. Copyright © 2008 John Wiley & Sons, Ltd.