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Iterative Methods for Solving Nonlinear Equations and Systems

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ISBN: 9783039219407 9783039219414 Year: Pages: 494 DOI: 10.3390/books978-3-03921-941-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-01-07 09:08:26
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Abstract

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.

Keywords

point projection --- intersection --- parametric curve --- n-dimensional 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 --- Newton-like 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 --- non-differentiable operator --- Lipschitz condition --- high order --- sixteenth order convergence method --- local convergence --- dynamics --- Banach space --- Newton’s method --- semi-local convergence --- Kantorovich hypothesis --- iterative methods --- Steffensen’s method --- R-order --- with memory --- computational efficiency --- non-linear equation --- basins of attraction --- optimal order --- higher order method --- computational order of convergence --- nonlinear equations --- multiple roots --- Chebyshev–Halley-type --- 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 --- multi-valued quasi-nonexpasive mappings --- Hilbert space --- sixteenth-order optimal convergence --- multiple-root 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 --- Newton-type 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 --- Newton-HSS method --- nonlinear HSS-like method --- Picard-HSS 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

Recent Advances in Mechanics of Non-Newtonian Fluids

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ISBN: 9783039283088 9783039283095 Year: Pages: 252 DOI: 10.3390/books978-3-03928-309-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-04-07 23:07:08
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Non-Newtonian (non-linear) fluids are common in nature, for example, in mud and honey, but also in many chemical, biological, food, pharmaceutical, and personal care processing industries. This Special Issue of Fluids is dedicated to the recent advances in the mathematical and physical modeling of non-linear fluids with industrial applications, especially those concerned with CFD studies. These fluids include traditional non-Newtonian fluid models, electro- or magneto-rheological fluids, granular materials, slurries, drilling fluids, polymers, blood and other biofluids, mixtures of fluids and particles, etc.

Keywords

inhomogeneous fluids --- non-newtonian fluids --- lubrication approximation (76A05, 76D08, 76A20) --- particle interaction --- viscoplastic fluid --- Bingham fluid --- computational fluid dynamics --- porous media --- convection --- Bingham fluid --- yield stress --- channel flow --- power-law fluid --- shear-dependent viscosity --- Reynolds equation --- lubrication approximation --- lid-driven cavity --- projection method --- shear-thinning --- aspect ratio --- Re numbers --- Brinkman equation --- viscosity ratio --- first- and second-order slip --- similarity transformation --- porous medium --- generalised simplified PTT --- Phan-Thien–Tanner (PTT) model --- Mittag–Leffler --- Couette flow --- Poiseuille–Couette flow --- non-isothermal flows --- creeping flows --- viscous fluid --- optimal control --- boundary control --- pressure boundary conditions --- weak solution --- existence theorem --- marginal function --- hemoglobin --- biological capacitor --- non-equilibrium thermodynamics --- hemoglobe capacitor --- thermodynamic capacitor --- smoothed particle hydrodynamics (SPH) --- meshless --- fluid-solid interaction (FSI) --- membrane --- rupture --- SPH-FEM --- stokesian dynamics --- dense suspension --- rheology --- bubble suspension --- suspension viscosity --- Gamma densitometer --- high viscosity oil --- slug translational velocity --- closure relationship --- wormlike micellar solutions (WMS) --- enhanced oil recovery (EOR) --- chemical EOR (cEOR) --- viscoelastic surfactants (VES) --- non-linear fluids --- variable viscosity --- natural convection --- convection-diffusion --- buoyancy force --- lubrication --- suspensions --- viscoplastic fluids --- cement --- biofluids --- oil recovery --- porous media

Multi-Sensor Information Fusion

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ISBN: 9783039283026 9783039283033 Year: Pages: 602 DOI: 10.3390/books978-3-03928-303-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-04-07 23:07:09
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This book includes papers from the section “Multisensor Information Fusion”, from Sensors between 2018 to 2019. It focuses on the latest research results of current multi-sensor fusion technologies and represents the latest research trends, including traditional information fusion technologies, estimation and filtering, and the latest research, artificial intelligence involving deep learning.

Keywords

linear regression --- covariance matrix --- data association --- sensor fusing --- SLAM --- multi-sensor data fusion --- conflicting evidence --- Dempster–Shafer evidence theory --- belief entropy --- similarity measure --- data classification --- fault diagnosis --- Bar-Shalom Campo --- Covariance Projection method --- data fusion --- distributed architecture --- Kalman filter --- linear constraints --- inconsistent data --- user experience evaluation --- user experience measurement --- eye-tracking --- facial expression --- galvanic skin response --- EEG --- interaction tracker --- self-reporting --- user experience platform --- mix-method approach --- image fusion --- multi-focus --- weight maps --- gradient domain --- fast guided filter. --- Dempster-Shafer evidence theory (DST) --- uncertainty measure --- open world --- closed world --- Deng entropy --- extended belief entropy --- sensor data fusion --- orthogonal redundant inertial measurement units --- data fusion architectures --- sensors bias --- fire source localization --- dynamic optimization --- global information --- the Range-Point-Range frame --- the Range-Range-Range frame --- sensor array --- SINS/DVL integrated navigation --- unscented information filter --- square root --- state probability approximation --- most suitable parameter form --- deep learning --- data preprocessing --- Human Activity Recognition (HAR) --- Internet of things (IoT) --- Industry 4.0 --- trajectory reconstruction --- low-cost sensors --- embedded systems --- powered two wheels (PTW) --- safe trajectory --- data fusion --- health management decision --- grey group decision-making --- health reliability degree --- maintenance decision --- sensor system --- least-squares filtering --- least-squares smoothing --- networked systems --- random parameter matrices --- random delays --- packet dropouts --- multi-sensor system --- multi-sensor information fusion --- particle swarm optimization --- sensor data fusion algorithm --- distributed intelligence system --- multi-sensor time series --- deep learning --- machine health monitoring --- time-distributed ConvLSTM model --- spatiotemporal feature learning --- optimal estimate --- unknown inputs --- distributed fusion --- augmented state Kalman filtering (ASKF) --- soft sensor --- coefficient of determination maximization strategy --- expectation maximization (EM) algorithm --- Gaussian mixture model (GMM) --- alumina concentration --- multi-sensor joint calibration --- high-dimensional fusion data (HFD) --- supervoxel --- Gaussian density peak clustering --- sematic segmentation --- multisensor data fusion --- multitarget tracking --- GMPHD --- sonar network --- RFS --- attitude estimation --- Kalman filter --- land vehicle --- magnetic angular rate and gravity (MARG) sensor --- quaternion --- yaw estimation --- network flow theory --- multitarget tracking --- spectral clustering --- A* search algorithm --- RTS smoother --- integer programming --- Surface measurement --- multi-sensor measurement --- surface modelling --- data fusion --- Gaussian process --- multi-sensor network --- observable degree analysis --- information fusion --- nonlinear system --- hybrid adaptive filtering --- weighted fusion estimation --- square-root cubature Kalman filter --- information filter --- surface quality control --- multi-sensor data fusion --- cutting forces --- vibration --- acoustic emission --- signal feature extraction methods --- predictive modeling techniques --- attitude --- orientation --- estimation --- Kalman filter --- quaternion --- manifold --- image registration --- evidential reasoning --- belief functions --- uncertainty --- DoS attack --- industrial cyber-physical system (ICPS) --- security zones --- mimicry security switch strategy --- fixed-point filter --- extended Kalman filter --- nested iterative method --- Steffensen’s iterative method --- convergence condition --- vehicular localization --- target positioning --- high-definition map --- vehicle-to-everything --- intelligent and connected vehicles --- intelligent transport system --- image registration --- non-rigid feature matching --- local structure descriptor --- Gaussian mixture model --- aircraft pilot --- workload --- multi-source data fusion --- fuzzy neural network --- principal component analysis --- parameter learning --- drift compensation --- domain adaption --- feature representations --- electronic nose --- data fusion --- dual gating --- MEMS accelerometer and gyroscope --- cardiac PET --- out-of-sequence --- multi-target tracking --- random finite set --- gaussian mixture probability hypothesis density --- multisensor system --- Gaussian process regression --- Bayesian reasoning method --- Dempster–Shafer evidence theory (DST) --- uncertainty measure --- novel belief entropy --- multi-sensor data fusion --- decision-level sensor fusion --- electronic nose --- subspace alignment --- interference suppression --- transfer --- evidence combination --- time-domain data fusion --- object classification --- uncertainty --- multirotor UAV --- precision landing --- artificial marker --- pose estimation --- sensor fusion --- camera --- LiDAR --- calibration --- plane matching --- ICP --- projection --- data fusion --- data registration --- adaptive distance function --- complex surface measurement --- Gaussian process model --- Dempster–Shafer evidence theory --- conflict measurement --- mutual support degree --- Hellinger distance --- Pignistic vector angle --- multi-sensor data fusion --- multi-environments --- state estimation --- unmanned aerial vehicle

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