# Jasmina Mansour: Att lösa femtegradsekvationen: En jämförelse av Newton-Raphsons och Bring-Jerrards metoder

## Bachelor thesis presentation

**Time: **
Mon 2022-08-22 09.00 - 10.00

**Location: **
Albano, House 1, Room T

**Respondent: **
Jasmina Mansour

**Abstract:**

This essay consists of a literary study of two methods for solving quintic equations: the Newton-Raphson method and the Bring-Jerrard method. In the latter, we will also use Tschirnhaus transformation, the Lagrange inversion theorem, as well as Newton’s binominal theorem. Each method will be presented with a corresponding equation that exemplifies their respective procedure in application. The essay concludes with a comparative discussion of difficulties in applying the respective methods. The Newton-Raphson method suffers from problems of how to find viable initial starting points so that the process converges fast enough. In contrast, the Bring-Jerrard method has the issue of though producing an exact expression, this expression may still converge too slowly, and have to be continued by analytic continuation.