2014.59: Generalized rational Krylov decompositions with an application to rational approximation
2014.59: Mario Berljafa and Stefan Güttel (2014) Generalized rational Krylov decompositions with an application to rational approximation.
This is the latest version of this eprint.
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
Generalized rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. We study the algebraic properties of such decompositions and present an implicit Q theorem for rational Krylov spaces. Transformations on rational Krylov decompositions allow for changing the poles of a rational Krylov space without recomputation, and two algorithms are presented for this task. Using such transformations we develop a rational Krylov method for rational least squares fitting. Numerical experiments indicate that the proposed method converges fast and robustly. A MATLAB toolbox with implementations of the presented algorithms and experiments is provided.
|Item Type:||MIMS Preprint|
All algorithms and numerical experiments presented in this paper are contained in a MATLAB toolbox available for download from http://guettel.com/rktoolbox
|Uncontrolled Keywords:||rational Krylov decomposition, inverse eigenvalue problem, rational approximation|
|Subjects:||MSC 2000 > 15 Linear and multilinear algebra; matrix theory|
MSC 2000 > 30 Functions of a complex variable
MSC 2000 > 65 Numerical analysis
|Deposited By:||Stefan Güttel|
|Deposited On:||31 March 2015|
Available Versions of this Item
- Generalized rational Krylov decompositions with an application to rational approximation (deposited 31 March 2015) [Currently Displayed]