The second-order Arnoldi (SOAR) procedure is an algorithm for computing an orthonormal basis of the second-order Krylov subspace. It has found applications in solving quadratic eigenvalue problems and model order reduction of second-order dynamical systems among others. Unfortunately, the SOAR procedure can be numerically unstable. The two-level orthogonal Arnoldi (TOAR) procedure has been proposed as an alternative to SOAR to cure the numerical instability. In this paper, we provide a rigorous stability analysis of the TOAR procedure. We prove that under mild assumptions, the TOAR procedure is backward stable in computing an orthonormal basis of the associated linear Krylov subspace. The benefit of the backward stability of TOAR is demonstrated by its high accuracy in structure-preserving model order reduction of second-order dynamical systems.
|Number of pages||20|
|Journal||SIAM Journal on Matrix Analysis and Applications|
|State||Published - 2016|
Bibliographical noteFunding Information:
School of Mathematical Sciences, Fudan University, Shanghai 200433, China (email@example.com, firstname.lastname@example.org). Part of this work was done while the first author was visiting the University of California, Davis, supported by China Scholarship Council. The research of the second author was supported in part by the Innovation Program of Shanghai Municipal Education Commission 13zz007, E-Institutes of Shanghai Municipal Education Commission N.E303004, and NSFC key project 91330201. ?Department of Computer Science and Department of Mathematics, University of California, Davis, CA 95616, USA (email@example.com). The research of the this author was supported in part by the NSF grants DMS-1522697 and CCF-1527091.
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- Backward stability
- Dynamical systems
- Model order reduction
- Second-order Arnoldi procedure
- Second-order Krylov subspace
ASJC Scopus subject areas