{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T12:11:51Z","timestamp":1780315911711,"version":"3.54.1"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["81101049"],"award-info":[{"award-number":["81101049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61271071"],"award-info":[{"award-number":["61271071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12PJ1401200"],"award-info":[{"award-number":["12PJ1401200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20110071 120019"],"award-info":[{"award-number":["20110071 120019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11MS007"],"award-info":[{"award-number":["11MS007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["81101049"],"award-info":[{"award-number":["81101049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61271071"],"award-info":[{"award-number":["61271071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12PJ1401200"],"award-info":[{"award-number":["12PJ1401200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20110071 120019"],"award-info":[{"award-number":["20110071 120019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11MS007"],"award-info":[{"award-number":["11MS007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Pujiang Talent Program","award":["81101049"],"award-info":[{"award-number":["81101049"]}]},{"name":"Shanghai Pujiang Talent Program","award":["61271071"],"award-info":[{"award-number":["61271071"]}]},{"name":"Shanghai Pujiang Talent Program","award":["12PJ1401200"],"award-info":[{"award-number":["12PJ1401200"]}]},{"name":"Shanghai Pujiang Talent Program","award":["20110071 120019"],"award-info":[{"award-number":["20110071 120019"]}]},{"name":"Shanghai Pujiang Talent Program","award":["11MS007"],"award-info":[{"award-number":["11MS007"]}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["81101049"],"award-info":[{"award-number":["81101049"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["61271071"],"award-info":[{"award-number":["61271071"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["12PJ1401200"],"award-info":[{"award-number":["12PJ1401200"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["20110071 120019"],"award-info":[{"award-number":["20110071 120019"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["11MS007"],"award-info":[{"award-number":["11MS007"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","award":["81101049"],"award-info":[{"award-number":["81101049"]}],"id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","award":["61271071"],"award-info":[{"award-number":["61271071"]}],"id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","award":["12PJ1401200"],"award-info":[{"award-number":["12PJ1401200"]}],"id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","award":["20110071 120019"],"award-info":[{"award-number":["20110071 120019"]}],"id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003347","name":"Fudan University","doi-asserted-by":"publisher","award":["11MS007"],"award-info":[{"award-number":["11MS007"]}],"id":[{"id":"10.13039\/501100003347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Partial fraction expansion (pfe) is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles.<\/jats:p>","DOI":"10.1155\/2014\/895036","type":"journal-article","created":{"date-parts":[[2014,10,12]],"date-time":"2014-10-12T17:05:20Z","timestamp":1413133520000},"page":"1-18","source":"Crossref","is-referenced-by-count":11,"title":["Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions"],"prefix":"10.1155","volume":"2014","author":[{"given":"Youneng","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Fudan University, Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinhua","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Fudan University, Shanghai 200433, China"},{"name":"Key Lab of Medical Imaging Computing and Computer Assisted Intervention of Shanghai, Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Fudan University, Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","year":"2010"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1974.1083830"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/1007073"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(83)90018-3"},{"key":"6","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/PROC.1969.6934","volume":"57","year":"1969","journal-title":"Proceedings of the IEEE"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084261"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/31.81863"},{"key":"10","first-page":"161","volume":"ct-11","year":"1964","journal-title":"IEEE Transactions on Circuit Theory"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(74)90056-8"},{"key":"12","doi-asserted-by":"crossref","first-page":"132","DOI":"10.2307\/27646303","volume":"37","year":"2006","journal-title":"The College Mathematics Journal"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.07.048"},{"key":"14","volume":"1","year":"2012","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"15","first-page":"647","volume":"12","year":"2013","journal-title":"WSEAS Transactions on Mathematics"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.10.016"},{"key":"17","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/TCSI.2013.2283998","volume":"61","year":"2014","journal-title":"IEEE Transactions on Circuits and Systems I"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1137\/0206040"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1137\/0206042"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(94)00037-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/895036.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/895036.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/895036.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T18:16:31Z","timestamp":1498155391000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/895036\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":18,"alternative-id":["895036","895036"],"URL":"https:\/\/doi.org\/10.1155\/2014\/895036","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}