{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T17:09:48Z","timestamp":1790788188827,"version":"4.1.0"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/I01912X\/1"],"award-info":[{"award-number":["EP\/I01912X\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The RKFIT algorithm outlined in [M. Berljafa and S. G\u00fcttel, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 894--916] is a Krylov-based approach for solving nonlinear rational least squares problems. This paper puts RKFIT into a general framework, allowing for its extension to nondiagonal rational approximants and a family of approximants sharing a common denominator. Furthermore, we derive a strategy for the degree reduction of the approximants, as well as methods for their conversion to partial fraction form, for the efficient evaluation, and for root-finding. We also discuss similarities and differences between RKFIT and the popular vector fitting algorithm. A MATLAB implementation of RKFIT is provided, and numerical experiments, including the fitting of a multiple-input\/multiple-output (MIMO) dynamical system and an optimization problem related to exponential integration, demonstrate its applicability.<\/jats:p>","DOI":"10.1137\/15m1025426","type":"journal-article","created":{"date-parts":[[2017,9,19]],"date-time":"2017-09-19T11:17:11Z","timestamp":1505819831000},"page":"A2049-A2071","source":"Crossref","is-referenced-by-count":84,"title":["The RKFIT Algorithm for Nonlinear Rational Approximation"],"prefix":"10.1137","volume":"39","author":[{"given":"Mario","family":"Berljafa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"G\u00fcttel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,19]]},"reference":[{"key":"atypb1","volume-title":"Ver. 3.8.3.8882","author":"Advanpix","year":"2015"},{"key":"atypb2","first-page":"193","volume-title":"CO, 1999), Contemp. 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Berljafa,\n                      Rational Krylov Decompositions: Theory and Applications\n                      , Ph.D. thesis, The University of Manchester, Manchester, UK, 2017, available online as MIMS EPrint 2017.6 athttp:\/\/eprints.ma.man.ac.uk\/2529\/."},{"key":"atypb5","volume-title":"MIMS EPrint","author":"Berljafa M.","year":"2014"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/140998081"},{"key":"atypb7","volume-title":"Filtering in the Time and Frequency Domains","author":"Blinchikoff H.","year":"1976"},{"key":"atypb8","volume-title":"Structured Matrix Based Methods for Approximate Polynomial GCD","volume":"15","author":"Boito P.","year":"2012"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1093\/gji\/ggv224"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61609-9"},{"key":"atypb11","volume-title":"MIMS EPrint","author":"Chahlaoui Y.","year":"2008"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/TADVP.2006.879429"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/LMWC.2008.922585"},{"key":"atypb14","volume-title":"Chebfun Guide","author":"Driscoll T. 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Gustavsen,\n                      Comments on \u201cA comparative study of vector fitting and orthonormal vector fitting techniques for EMC applications,''\n                      in Proceedings of the 18th International Zurich Symposium on Electromagnetic Compatibility, Zurich, Switzerland, 2007, pp. 131-134.","DOI":"10.1109\/EMCZUR.2007.4388213"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/61.772353"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1002\/gamm.201310002"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0312(200008)53:8<1039::AID-CPA4>3.0.CO;2-I"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1145\/355900.355912"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1109\/TMTT.2013.2246526"},{"key":"atypb31","first-page":"37","volume":"4","author":"Levy E. 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