Premium
A Greedy Subspace Method for Computing the ℒ ∞ ‐Norm
Author(s) -
Aliyev Nicat,
Benner Peter,
Mengi Emre,
Schwerdtner Paul,
Voigt Matthias
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710343
Subject(s) - linear subspace , subspace topology , computation , norm (philosophy) , mathematics , interpolation (computer graphics) , projection (relational algebra) , mathematical optimization , focus (optics) , function (biology) , algorithm , computer science , algebra over a field , pure mathematics , mathematical analysis , artificial intelligence , motion (physics) , physics , optics , political science , evolutionary biology , biology , law
We consider the computation of the ℒ ∞ ‐norm for a general class of ℒ ∞ ‐functions and focus on the case where the function is represented in terms of large‐scale matrix‐valued factors. We propose a subspace projection method to obtain reduced approximations of this function by interpolation techniques. The ℒ ∞ ‐norms are computed for the resulting reduced functions, then the subspaces are refined by means of the optimizer of the ℒ ∞ ‐norm of the reduced function. In this way we obtain much better performance compared to existing methods. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom