A Greedy Subspace Method for Computing the ℒ∞‐Norm. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Aliyev, Nicat; Benner, Peter; Mengi, Emre; Schwerdtner, Paul; Voigt, Matthias
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 751
• Page End: 752
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710343
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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)