×

Algorithms for the rational approximation of matrix-valued functions. (English) Zbl 07395803


MSC:

65D15 Algorithms for approximation of functions
41A20 Approximation by rational functions
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] SLICOT Benchmark Examples for Model Reduction, http://slicot.org/20-site/126-benchmark-examples-for-model-reduction, 2002.
[2] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Adv. Des. Control 6, SIAM, Philadelphia, 2005, https://doi.org/10.1137/1.9780898718713. · Zbl 1112.93002
[3] A. C. Antoulas, C. A. Beattie, and S. Gugercin, Interpolatory model reduction of large-scale dynamical systems, in Efficient Modeling and Control of Large-Scale Systems, Springer, Boston, MA, 2010, pp. 3-58. · Zbl 1229.65103
[4] A. C. Antoulas, C. A. Beattie, and S. Gugercin, Interpolatory Methods for Model Reduction, Comput. Sci. Engrg. 21, SIAM, Philadelphia, 2020, https://doi.org/10.1137/1.9781611976083. · Zbl 1319.93016
[5] A. C. Antoulas, I. V. Gosea, and A. C. Ionita, Model reduction of bilinear systems in the Loewner framework, SIAM J. Sci. Comput., 38 (2016), pp. B889-B916, https://doi.org/10.1137/15M1041432. · Zbl 06645409
[6] A. C. Antoulas, S. Lefteriu, and A. C. Ionita, A tutorial introduction to the Loewner framework for model reduction, in Model Reduction and Approximation, Comput. Sci. Engrg. 15, SIAM, Philadelphia, 2017, pp. 335-376, https://doi.org/10.1137/1.9781611974829.ch8.
[7] M. Berljafa, S. Elsworth, and S. Güttel, A Rational Krylov Toolbox for MATLAB, MIMS EPrint 2014.56, Manchester Institute for Mathematical Sciences, The University of Manchester, Manchester, UK, 2014, http://rktoolbox.org/.
[8] M. Berljafa and S. Güttel, Generalized rational Krylov decompositions with an application to rational approximation, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 894-916, https://doi.org/10.1137/140998081. · Zbl 1319.65028
[9] M. Berljafa and S. Güttel, The RKFIT algorithm for nonlinear rational approximation, SIAM J. Sci. Comput., 39 (2017), pp. A2049-A2071, https://doi.org/10.1137/15M1025426. · Zbl 1373.65037
[10] J.-P. Berrut and L. N. Trefethen, Barycentric Lagrange interpolation, SIAM Rev., 46 (2004), pp. 501-517, https://doi.org/10.1137/S0036144502417715. · Zbl 1061.65006
[11] Y. Chahlaoui and P. Van Dooren, Benchmark examples for model reduction of linear time-invariant dynamical systems, in Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. 45, Springer, Berlin, 2005, pp. 379-392. · Zbl 1100.93006
[12] T. A. Driscoll, N. Hale, and L. N. Trefethen, Chebfun Guide, https://www.chebfun.org/docs/guide/, 2014.
[13] Z. Drmač, S. Gugercin, and C. Beattie, Vector fitting for matrix-valued rational approximation, SIAM J. Sci. Comput., 37 (2015), pp. A2346-A2379, https://doi.org/10.1137/15M1010774. · Zbl 1323.93050
[14] S. Elsworth and S. Güttel, Conversions between barycentric, RKFUN, and Newton representations of rational interpolants, Linear Algebra Appl., 576 (2019), pp. 246-257. · Zbl 1429.65075
[15] K. Gallivan, A. Vandendorpe, and P. Van Dooren, Model reduction of MIMO systems via tangential interpolation, SIAM J. Matrix Anal. Appl., 26 (2004), pp. 328-349, https://doi.org/10.1137/S0895479803423925. · Zbl 1078.41016
[16] B. Gustavsen, Improving the pole relocating properties of vector fitting, IEEE Trans. Power Delivery, 21 (2006), pp. 1587-1592.
[17] B. Gustavsen, Matrix Fitting Toolbox, https://www.sintef.no/projectweb/vectorfitting/downloads/matrix-fitting-toolbox/, 2009.
[18] B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Trans. Power Delivery, 14 (1999), pp. 1052-1061.
[19] S. Güttel and F. Tisseur, The nonlinear eigenvalue problem, Acta Numer., 26 (2017), pp. 1-94. · Zbl 1377.65061
[20] N. J. Higham, G. M. Negri Porzio, and F. Tisseur, An updated set of nonlinear eigenvalue problems, Tech. Report MIMS EPrint 2019.5, Manchester, United Kingdom, 2019. http://eprints.maths.manchester.ac.uk/.
[21] A. Hochman, FastAAA: A fast rational-function fitter, in Proceedings of the 26th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS) (San Jose, CA), IEEE, Washington, DC, 2017, pp. 1-3.
[22] D. S. Karachalios, I. V. Gosea, and A. C. Antoulas, The Loewner framework for system identification and reduction, in Handbook on Model Reduction Volume 1: Methods and Algorithms, De Gruyter, Berlin, to appear.
[23] P. Lietaert, J. Pérez, B. Vandereycken, and K. Meerbergen, Automatic Rational Approximation and Linearization of Nonlinear Eigenvalue Problems, preprint, https://arxiv.org/abs/1801.08622, 2018.
[24] A. J. Mayo and A. C. Antoulas, A framework for the solution of the generalized realization problem, Linear Algebra Appl., 425 (2007), pp. 634-662. · Zbl 1118.93029
[25] Y. Nakatsukasa, O. Sète, and L. N. Trefethen, The AAA algorithm for rational approximation, SIAM J. Sci. Comput., 40 (2018), pp. A1494-A1522, https://doi.org/10.1137/16M1106122. · Zbl 1390.41015
[26] A. Ruhe, Rational Krylov sequence methods for eigenvalue computation, Linear Algebra Appl., 58 (1984), pp. 391-405, https://doi.org/10.1016/0024-3795(84)90221-0. · Zbl 0554.65025
[27] R. Van Beeumen, W. Michiels, and K. Meerbergen, Linearization of Lagrange and Hermite interpolating matrix polynomials, IMA J. Numer. Anal., 35 (2015), pp. 909-930. · Zbl 1314.41002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.