Analytical solution of polynomial equations with an application to the Quintic equation

Anastasselou, EG; Panayotounakos, DE

dc.contributor.author	Anastasselou, EG	en
dc.contributor.author	Panayotounakos, DE	en
dc.date.accessioned	2014-03-01T01:06:44Z
dc.date.available	2014-03-01T01:06:44Z
dc.date.issued	1987	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9606
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-45949128808&partnerID=40&md5=ab23accf5d3dcf4054ac1b8ed7a49f69	en
dc.subject.classification	Mathematics, Applied	en
dc.title	Analytical solution of polynomial equations with an application to the Quintic equation	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1987	en
heal.abstract	A recently proposed method for the derivation of exact analytical integral formulae for the zeros of analytic functions (based on the simple discontinuity problem for a sectionally analytic function along the real axis) is applied here to the case of polynomials. The peculiarity of the present application is that the integrals appearing in the closed-form formulae for the sought zeros are interpreted as Cauchy-type principal-value integrals or even as finite-part integrals. The case of the quintic equation with real coefficients is considered in some detail, and it is shown that the roots of this equation can always be obtained in closed form. Numerical results for this equation are also presented. Equations of higher degree can also be solved in closed form under appropriate conditions. © 1987.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.isi	ISI:A1987F581100004	en
dc.identifier.volume	21	en
dc.identifier.issue	2	en
dc.identifier.spage	145	en
dc.identifier.epage	155	en