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Iterative Methods for Solving Nonlinear Equations and Systems
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
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Keywords
- ?-continuity condition
- accretive operators
- asymptotic error constant
- attractor basin
- Banach space
- basin of attraction
- basins of attraction
- Chebyshev–Halley-type
- computational efficiency
- computational efficiency index
- computational order of convergence
- conjugate gradient method
- convex constraints
- convexity
- divided difference operator
- drazin inverse
- Dynamics
- efficiency index
- engineering applications
- error bound
- finite difference (FD)
- fixed point theorem
- fourth order iterative methods
- Fréchet derivative
- Fredholm integral equation
- generalized inverse
- global convergence
- heston model
- high order
- higher order
- higher order method
- higher order of convergence
- Hilbert space
- Hull–White
- integral equation
- intersection
- iteration scheme
- iterative method
- iterative methods
- iterative process
- Jarratt method
- Kantorovich hypothesis
- King’s family
- Kung–Traub conjecture
- least square problem
- Lipschitz condition
- local convergence
- Moore–Penrose
- multi-valued quasi-nonexpasive mappings
- Multiple roots
- multiple zeros
- multiple-root finder
- multipoint iterations
- multipoint iterative methods
- n-dimensional Euclidean space
- Newton method
- Newton-HSS method
- Newton-like method
- Newton-type methods
- Newton’s iterative method
- Newton’s method
- Newton’s second order method
- non-differentiable operator
- non-linear equation
- nonlinear equation
- nonlinear equations
- nonlinear HSS-like method
- nonlinear models
- nonlinear monotone equations
- nonlinear operator equation
- Nonlinear systems
- numerical experiment
- Optimal iterative methods
- optimal methods
- optimal order
- option pricing
- order of convergence
- Padé approximation
- parametric curve
- PDE
- Picard-HSS method
- planar algebraic curve
- point projection
- Potra–Pták method
- projection method
- purely imaginary extraneous fixed point
- R-order
- radius of convergence
- rate of convergence
- rectangular matrices
- semi-local convergence
- semilocal convergence
- signal and image processing
- Signal processing
- sixteenth order convergence method
- sixteenth-order optimal convergence
- smooth and nonsmooth operators
- split variational inclusion problem
- Steffensen’s method
- system of nonlinear equations
- systems of nonlinear equations
- the improved curvature circle algorithm
- variational inequality problem
- weight function
- with memory
Links
DOI: 10.3390/books978-3-03921-941-4Editions
