Efficient algorithm for simultaneous reduction to the $$m$$ m -Hessenberg-triangular-triangular form
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0516-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0516-y | ||
| 100 | 1 | |a Bosner |D Nela |u Department of Mathematics, University of Zagreb, Zagreb, Croatia |4 aut | |
| 245 | 1 | 0 | |a Efficient algorithm for simultaneous reduction to the $$m$$ m -Hessenberg-triangular-triangular form |h [Elektronische Daten] |c [Nela Bosner] |
| 520 | 3 | |a This paper proposes an efficient algorithm for simultaneous reduction of three matrices by using orthogonal transformations, where $$A$$ A is reduced to $$m$$ m -Hessenberg form, and $$B$$ B and $$E$$ E to triangular form. The algorithm is a blocked version of the algorithm described by Miminis and Paige (Int J Control 35:341-354, 1982). The $$m$$ m -Hessenberg-triangular-triangular form of matrices $$A$$ A , $$B$$ B and $$E$$ E is specially suitable for solving multiple shifted systems $$(\sigma E-A)X=B$$ ( σ E - A ) X = B . Such shifted systems naturally occur in control theory when evaluating the transfer function of a descriptor system, or in interpolatory model reduction methods. They also arise as a result of discretizing the time-harmonic wave equation in heterogeneous media, or originate from structural dynamics engineering problems. The proposed blocked algorithm for the $$m$$ m -Hessenberg-triangular-triangular reduction is based on aggregated Givens rotations, and is a generalization of the blocked algorithm for the Hessenberg-triangular reduction proposed by Kågström et al. (BIT 48:563-584, 2008). Numerical tests confirm that the blocked algorithm is much faster than its non-blocked version based on regular Givens rotations only. As an illustration of its efficiency, two applications of the $$m$$ m -Hessenberg-triangular-triangular reduction from control theory are described: evaluation of the transfer function of a descriptor system at many complex values, and computation of the staircase form used to identify the controllable part of the system. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a $$m$$ m -Hessenberg-triangular-triangular form |2 nationallicence | |
| 690 | 7 | |a Orthogonal transformations |2 nationallicence | |
| 690 | 7 | |a Level 3 BLAS |2 nationallicence | |
| 690 | 7 | |a Blocked algorithm |2 nationallicence | |
| 690 | 7 | |a Solving shifted system |2 nationallicence | |
| 690 | 7 | |a Transfer function evaluation |2 nationallicence | |
| 690 | 7 | |a Staircase form |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 677-703 |x 0006-3835 |q 55:3<677 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0516-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0516-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Bosner |D Nela |u Department of Mathematics, University of Zagreb, Zagreb, Croatia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 677-703 |x 0006-3835 |q 55:3<677 |1 2015 |2 55 |o 10543 | ||