{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T19:53:36Z","timestamp":1765828416021,"version":"3.41.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>\n            Calculation of the scaled complex error function\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(w(z)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            by recurrence is discussed, and a new method for determining the number of steps required to achieve a given accuracy is introduced. This method is found to work throughout the complex plane, except for a short section of the real line, centred at the origin. An algorithm based on this analysis is implemented; Taylor series with stored coefficients are used to compute\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(w(z)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            in a small region where recurrence is not efficient. The new algorithm is tested extensively and found to outperform earlier recurrence-based codes. It also performs favourably against recent codes based on other methods.\n          <\/jats:p>","DOI":"10.1145\/3688799","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T00:37:30Z","timestamp":1724287050000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Algorithm 1046: An Improved Recurrence Method for the Scaled Complex Error Function"],"prefix":"10.1145","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-450X","authenticated-orcid":false,"given":"Ian","family":"Thompson","sequence":"first","affiliation":[{"name":"Mathematical Sciences, University of Liverpool, Liverpool, UK"}]}],"member":"320","published-online":{"date-parts":[[2024,10,25]]},"reference":[{"key":"e_1_3_1_2_2","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz M.","year":"1965","unstructured":"M. Abramowitz and I. A. Stegun. 1965. 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Pitman, London."},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1145\/2806884"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1145\/3309681"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1145\/2049673.2049679"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3688799","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3688799","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:04:09Z","timestamp":1750291449000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3688799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9,30]]}},"alternative-id":["10.1145\/3688799"],"URL":"https:\/\/doi.org\/10.1145\/3688799","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2024,9,30]]},"assertion":[{"value":"2023-06-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-06-24","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-10-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}