The New New-Nacci Method for Calculating the Roots of a Univariate Polynomial and Solution of Quintic Equation in Radicals

Једноставна страница ставке
dc.citation.spage746
dc.citation.volume8
dc.contributor.authorTanackov, Ilija
dc.contributor.authorPavkov, Ivan
dc.contributor.authorStević, Željko
dc.date.accessioned2023-07-04T12:39:03Z
dc.date.available2023-07-04T12:39:03Z
dc.date.issued2020
dc.description.abstractAn arbitrary univariate polynomial of nth degree has n sequences. The sequences are systematized into classes. All the values of the first class sequence are obtained by Newton’s polynomial of nth degree. Furthermore, the values of all sequences for each class are calculated by Newton’s identities. In other words, the sequences are formed without calculation of polynomial roots. The New-nacci method is used for the calculation of the roots of an nth-degree univariate polynomial using radicals and limits of successive members of sequences. In such an approach as is presented in this paper, limit play a catalytic–theoretical role. Moreover, only four basic algebraic operations are sufficient to calculate real roots. Radicals are necessary for calculating conjugated complex roots. The partial limitations of the New-nacci method may appear from the decadal polynomial. In the case that an arbitrary univariate polynomial of nth degree (n 10) has five or more conjugated complex roots, the roots of the polynomial cannot be calculated due to Abel’s impossibility theorem. The second phase of the New-nacci method solves this problem as well. This paper is focused on solving the roots of the quintic equation. The method is verified by applying it to the quintic polynomial with all real roots and the Degen–Abel polynomial, dating from 1821.
dc.identifier.doi10.3390/math8050746
dc.identifier.urihttps://vaseljena.ues.rs.ba/handle/123456789/343
dc.language.isoen
dc.publisherMDPI
dc.sourceMathematics
dc.subjectnonlinear approximate method; quintic equation; Pentanacci sequence; Abel’s impossibility theorem
dc.titleThe New New-Nacci Method for Calculating the Roots of a Univariate Polynomial and Solution of Quintic Equation in Radicals
dc.typeArticle
Датотеке
Оригинални завежљај
Сада се приказује 1 - 1 од 1
Сличица
Име:
The New New-Nacci Method for Calculating the.pdf
Величина:
830.83 KB
Формат:
Adobe Portable Document Format
Опис:
Преузимање
Свежањ лиценце
Сада се приказује 1 - 1 од 1
Сличица
Име:
license.txt
Величина:
1.71 KB
Формат:
Item-specific license agreed to upon submission
Опис:
Преузимање
Колекције
Саобраћајни факултет [Научни радови] / Faculty of Transport and Traffic Engineering [Scientific papers]