{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:24Z","timestamp":1760149764185,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,9]],"date-time":"2023-09-09T00:00:00Z","timestamp":1694217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Vicerrectorado de Investigaci\u00f3n de la Universitat Polit\u00e8cnica de Val\u00e8ncia","award":["PAID-11-22"],"award-info":[{"award-number":["PAID-11-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and\/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to matrix logarithm computation and using the Romberg integration method, together with the inverse scaling and squaring technique. This novel method was implemented and compared with three different state-of-the-art codes, all based on Pad\u00e9 approximation. The experimental results, under a heterogeneous matrix test battery, showed that the new method was numerically stable, with an elapsed time midway among the other codes, and it generally offered a higher accuracy.<\/jats:p>","DOI":"10.3390\/a16090434","type":"journal-article","created":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T09:09:21Z","timestamp":1694423361000},"page":"434","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computing the Matrix Logarithm with the Romberg Integration Method"],"prefix":"10.3390","volume":"16","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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Higham, N.J. 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