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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 nontrivial 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.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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This book includes papers in crossdisciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cuttingedge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a mustread for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.
human behaviour  organisational risk  multicriteria decisionmaking  DEMATEL  bottling process  cellular automata  game of life  brain dynamics  random nonautonomous second order linear differential equation  mean square analytic solution  random power series  uncertainty quantification  systems of nonlinear equations  iterative methods  Newton’s method  order of convergence  computational efficiency  basin of attraction  F110 frigate  decisionmaking  ASW  antitorpedo decoy  AHP  uncertainty modelling  Chikungunya disease  mathematical modeling  nonlinear dynamical systems  numerical simulations  parameter estimation  Markov chain Monte Carlo  block preconditioner  generalized eigenvalue problem  neutron diffusion equation  modified block Newton method  bone repair  macrophages  immune system  cytokines  stem cells  exponential polynomial  discrete dynamical systems  convergence  Hidden Markov models  mathematical linguistics  Voynich Manuscript  IPV  violence index  independence index  model  ode
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A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.
Banach space  weightedNewton method  local convergence  Fréchetderivative  ball radius of convergence  Nondifferentiable operator  nonlinear equation  divided difference  Lipschitz condition  convergence order  local and semilocal convergence  scalar equations  computational convergence order  Steffensen’s method  basins of attraction  nonlinear equations  multipleroot solvers  Traub–Steffensen method  fast algorithms  Multiple roots  Optimal iterative methods  Scalar equations  Order of convergence  simple roots  Newton’s method  computational convergence order  nonlinear equations  split variational inclusion problem  generalized mixed equilibrium problem  fixed point problem  maximal monotone operator  left Bregman asymptotically nonexpansive mapping  uniformly convex and uniformly smooth Banach space  nonlinear equations  multiple roots  derivativefree method  optimal convergence  multiple roots  optimal iterative methods  scalar equations  order of convergence  Newton–HSS method  systems of nonlinear equations  semilocal convergence  local convergence  convergence order  Banach space  iterative method  nonlinear equations  Chebyshev’s iterative method  fractional derivative  basin of attraction  nonlinear equations  iterative methods  general means  basin of attraction
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