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A Modified Quadratic Interpolation Method for Root Finding
AbstractA modification of the quadratic interpolation method for finding the root of a continuous function is proposed. Two quadratic interpolation...
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Finding roots of complex analytic functions via generalized colleague matrices
We present a scheme for finding all roots of an analytic function in a square domain in the complex plane. The scheme can be viewed as a...
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Backtracking New Q-Newton’s Method, Newton’s Flow, Voronoi’s Diagram and Stochastic Root Finding
A new variant of Newton’s method - named Backtracking New Q-Newton’s method (BNQN) - which has strong theoretical guarantee, is easy to implement,...
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Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks
In this work, we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large-scale...
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Finding Root Spaces for a Linear Algebraic Spectral Problem
AbstractFor an algebraic spectral problem that is linear with respect to the spectral parameter, some numerical methods are considered to find the...
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Motif Finding Algorithms: A Performance Comparison
Network motifs are subgraphs of a network that occur more frequently than expected, according to some reasonable null model. They represent building...
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Dynamical and numerical analysis of classical multiple roots finding methods applied for different multiplicities
The aim of this paper is the study of the robustness of classical methods defined for finding multiple roots with single multiplicity m when they are...
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Complex Numbers and Complex Plane
In this chapter we recall some concepts from basic courses in mathematical analysis of real-valued functions of one and several variables as well as...
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A new class of derivative-free root solvers with increasing optimal convergence order and their complex dynamics
We present a general class of derivative free iterative methods with optimal order of convergence for solving nonlinear equations. The methodology is...
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Faber polynomial coefficient inequalities for bi-Bazilevič functions associated with the Fibonacci-number series and the square-root functions
Two new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are...
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Optimal Parameter Estimation Techniques for Complex Nonlinear Systems
Accurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This...
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Rolle Models in the Real and Complex World
Numerous problems of analysis (real and complex) and geometry (analytic, algebraic, Diophantine e.a.) can be reduced to calculation of the “number of...
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Finding the homology of manifolds using ellipsoids
A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider...
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Complex WKB Method (One-Dimensional Linear Problems on the Complex Plane)
AbstractThe survey is devoted to the complex WKB method which arose as an approach to describing the asymptotic behavior of solutions to...
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Complex dynamics of a sixth and seventh order family of root finding methods
This paper intends to investigate the dynamical behavior of a parameter based sixth and seventh order convergent family of iterative methods in the...
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Complex Analysis
Our idea of what a number is has evolved considerably throughout history. The ancients thought of numbers as extensions in space; we have looked at...
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Local and Semilocal Convergence of a Family of Multi-point Weierstrass-Type Root-Finding Methods
Weierstrass (Sitzungsber Königl Preuss Akad Wiss Berlin II:1085–1101, 1891) introduced his famous iterative method for numerical finding all zeros of...
