{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T22:23:13Z","timestamp":1780611793872,"version":"3.54.1"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006591","name":"Ministry of Industry, Energy and Tourism","doi-asserted-by":"publisher","award":["TIN2017-30489314-P"],"award-info":[{"award-number":["TIN2017-30489314-P"]}],"id":[{"id":"10.13039\/501100006591","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The action of the matrix exponential on a vector eAtv, A\u2208Cn\u00d7n, v\u2208Cn, appears in problems that arise in mathematics, physics, and engineering, such as the solution of systems of linear ordinary differential equations with constant coefficients. Nowadays, several state-of-the-art approximations are available for estimating this type of action. In this work, two Taylor algorithms are proposed for computing eAv, which make use of the scaling and recovering technique based on a backward or forward error analysis. A battery of highly heterogeneous test matrices has been used in the different experiments performed to compare the numerical and computational properties of these algorithms, implemented in the MATLAB language. In general, both of them improve on those already existing in the literature, in terms of accuracy and response time. Moreover, a high-performance computing version that is able to take advantage of the computational power of a GPU platform has been developed, making it possible to tackle high dimension problems at an execution time significantly reduced.<\/jats:p>","DOI":"10.3390\/a15020048","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T01:41:59Z","timestamp":1643420519000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Two Taylor Algorithms for Computing the Action of the Matrix Exponential on a Vector"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6912-4453","authenticated-orcid":false,"given":"Javier","family":"Ib\u00e1\u00f1ez","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6812-7364","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Alonso","sequence":"additional","affiliation":[{"name":"Instituto de Instrumentaci\u00f3n para Imagen Molecular, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6882-6592","authenticated-orcid":false,"given":"Pedro","family":"Alonso-Jord\u00e1","sequence":"additional","affiliation":[{"name":"Departamento de Sistemas Inform\u00e1ticos y Computaci\u00f3n, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3303-6371","authenticated-orcid":false,"given":"Emilio","family":"Defez","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8612-6717","authenticated-orcid":false,"given":"Jorge","family":"Sastre","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1080\/15427951.2014.971203","article-title":"Sublinear Column-wise Actions of the Matrix Exponential on Social Networks","volume":"11","author":"Gleich","year":"2015","journal-title":"Internet Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.cam.2019.01.015","article-title":"Analysis of Directed Networks via the Matrix Exponential","volume":"355","author":"Matar","year":"2019","journal-title":"J. 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