QDPA swMATH ID: 12759 Software Authors: Rommes, Joost; Martins, Nelson Description: Computing transfer function dominant poles of large-scale second-order dynamical systems. A new algorithm for the computation of dominant poles of transfer functions of large-scale second-order dynamical systems is presented: the quadratic dominant pole algorithm (QDPA). The algorithm works directly with the system matrices of the original system, so no linearization is needed. To improve global convergence, the QDPA uses subspace acceleration, and deflation of found dominant poles is implemented in a very efficient way. The dominant poles and corresponding eigenvectors can be used to construct structure-preserving modal approximations and also to improve reduced-order models computed by Krylov subspace methods, as is illustrated by numerical results. Homepage: https://sites.google.com/site/rommes/software Dependencies: Matlab Keywords: dominant poles; transfer function; quadratic eigenvalue problem; second-order dynamical systems; transfer function residues; model reduction; large-scale systems; sparse eigenanalysis; modal approximation; modal analysis; second-order Arnoldi method; rational Krylov subspace method; algorithm quadratic; dominant pole algorithm; global convergence; subspace acceleration; eigenvectors; numerical results Related Software: DPA_TDEFL; AAA; JDQZ; JDQR; COMSOL; SOLBT; MORLAB; mftoolbox; MESS; Loewner; RKToolbox; redbKIT; NLEVP; PETSc; SLEPc; PSAPSR; Algorithm 961; HIFOO; UMFPACK; IRAM Cited in: 9 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Computing transfer function dominant poles of large-scale second-order dynamical systems. Zbl 1168.65338Rommes, Joost; Martins, Nelson 2008 all top 5 Cited by 14 Authors 3 Rommes, Joost 2 Benner, Peter 2 Martins, Nelson 2 Meerbergen, Karl 2 Saadvandi, Maryam 1 Beattie, Christopher A. 1 Campos, Carmen 1 Desmet, Wim 1 Gugercin, Serkan 1 Jarlebring, Elias 1 Mitchell, Tim 1 Román, Jose E. 1 Tomljanović, Zoran 1 Werner, Steffen W. R. all top 5 Cited in 6 Serials 2 Linear Algebra and its Applications 2 SIAM Journal on Scientific Computing 1 BIT 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 Advances in Computational Mathematics all top 5 Cited in 6 Fields 7 Systems theory; control (93-XX) 4 Numerical analysis (65-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year