ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS
Mudassir Shams, Naila Rafiq, Nasreen Kausar, Praveen Agarwal, Nazir Ahmad Mir, Yongmin Li
Abstract
This paper develops optimal family of fourth-order iterative techniques in order to find a single root and to generalize them for simultaneous finding of all roots of polynomial equation. Convergence study reveals that for single root finding methods, its optimal convergence order is 4, while for simultaneous methods, it is 12. Computational cost and numerical illustrations demonstrate that the newly developed family of methods outperformed the previous methods available in the literature.
Topics & Concepts
Convergence (economics)MathematicsRoot (linguistics)Root-finding algorithmPolynomialApplied mathematicsOrder (exchange)Properties of polynomial rootsMathematical optimizationIterative methodRate of convergenceComputer scienceMatrix polynomialMathematical analysisNonlinear systemKey (lock)FinanceEconomic growthQuantum mechanicsLinguisticsPhysicsPhilosophyComputer securityEconomicsIterative Methods for Nonlinear EquationsMatrix Theory and AlgorithmsAdvanced Optimization Algorithms Research