𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Improving a method of search for solving polynomial equations

✍ Scribed by M. Hujter

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
136 KB
Volume
31
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

This paper is related to the Lehmer-Schur methods in numerical mathematics in the complex plane. It is shown that by a slight modification of the "optimized" Lehmer-Schur method of Gal~ntai, the "speed" quotient 0.6094 can be reduced to 0.5758. The crucial idea is based on a discrete geometrical observation Keywords--Complex polynomials, Finding zeros, Disks.

πŸ“œ SIMILAR VOLUMES

Improved Newton’s method with exact line
Improved Newton’s method with exact line searches to solve quadratic matrix equation
✍ Jian-hui Long; Xi-yan Hu; Lei Zhang πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 478 KB

In this paper, we study the matrix equation AX 2 + B X + C = 0, where A, B and C are square matrices. We give two improved algorithms which are better than Newton's method with exact line searches to calculate the solution. Some numerical examples are reported to illustrate our algorithms.

A Chebyshev Polynomial Interval-Searchin
A Chebyshev Polynomial Interval-Searching Method ("Lanczos Economization") for Solving a Nonlinear Equation with Application to the Nonlinear Eigenvalue Problem
✍ John P. Boyd πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 362 KB

To search a given real interval for roots, our algorithm is to replace \(f(\lambda)\) by \(f_{N}(\lambda)\), its \(N\)-term Chebyshev expansion on the search interval \(\lambda \in\left[\lambda_{\min }, \lambda_{\max }\right]\), and compute the roots of this proxy. This strategy is efficient if and

An improvement to homotopy perturbation
An improvement to homotopy perturbation method for solving system of linear equations
✍ ElΓ§in Yusufoğlu πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 344 KB

## Exact solution a b s t r a c t In this paper, we present an efficient numerical algorithm to find exact solutions for the system of linear equations based on homotopy perturbation method (HPM). A reliable modification is proposed, and the modified method is employed to solve the system of linea