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Encyclopedia of Applied and Computational Mathematics

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Cover of 'Encyclopedia of Applied and Computational Mathematics'

Table of Contents

  1. Altmetric Badge
    Book Overview
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    Chapter 1 Camassa–Holm Equations
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    Chapter 2 Adjoint Methods as Applied to Inverse Problems
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    Chapter 7 Boundary Control Method
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    Chapter 9 Invisibility Cloaking
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    Chapter 13 Elastography, Applications Using MRI Technology
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    Chapter 17 Factorization Method in Inverse Scattering
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    Chapter 19 Inhomogeneous Media Identification
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    Chapter 21 Inverse Spectral Problems: 1-D, Theoretical Results
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    Chapter 24 Inverse Boundary Problems for Electromagnetic Waves
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    Chapter 29 Inverse Nodal Problems: 1-D
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    Chapter 33 Inverse Spectral Problems: 1-D, Algorithms
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    Chapter 37 Linear Sampling
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    Chapter 38 Agent-Based Models in Infectious Disease and Immunology
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    Chapter 43 Optical Tomography: Applications
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    Chapter 44 Optical Tomography: Theory
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    Chapter 45 Inverse Optical Design
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    Chapter 46 Photonic Crystals and Waveguides: Simulation and Design
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    Chapter 48 Radar Imaging
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    Chapter 50 Random Media in Inverse Problems, Theoretical Aspects
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    Chapter 52 Regularization of Inverse Problems
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    Chapter 56 Molecular Dynamics
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    Chapter 60 Actin Cytoskeleton, Multi-scale Modeling
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    Chapter 62 Angiogenesis, Mathematical Modeling Perspective
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    Chapter 63 Applied Control Theory for Biological Processes
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    Chapter 66 Medical Imaging
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    Chapter 67 Cancer Initiation and Progression, Modeling
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    Chapter 68 Cell Biology Modeling Development
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    Chapter 69 Cell Migration, Biomechanics
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    Chapter 70 Cell-Based Modeling
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    Chapter 73 Heart Modeling
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    Chapter 75 Molecular Motor Dynamics, Modeling
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    Chapter 76 Moving Boundary Problems and Cancer
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    Chapter 78 Pattern Formation and Development
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    Chapter 82 Microlocal Analysis Methods
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    Chapter 83 Biofilm Structure and Function, Modeling
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    Chapter 84 Neural Spikes, Identification from a Multielectrode Array
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    Chapter 85 Epidemiology Modeling
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    Chapter 88 Molecular Dynamics Simulations
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    Chapter 90 Metabolic Networks, Modeling
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    Chapter 92 Computerized Tomography, ART
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    Chapter 94 Backward Differentiation Formulae
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    Chapter 96 Boundary Value Methods: GAMD, TOM
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    Chapter 98 Encyclopedia of Applied and Computational Mathematics
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    Chapter 100 Explicit Stabilized Runge–Kutta Methods
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    Chapter 102 Collocation Methods
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    Chapter 103 Composition Methods
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    Chapter 105 Defect Correction Methods
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    Chapter 106 Delay Differential Equations
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    Chapter 107 Dense Output
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    Chapter 110 Electrical Circuits
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    Chapter 111 Euler Methods, Explicit, Implicit, Symplectic
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    Chapter 112 Exponential Integrators
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    Chapter 114 Fer and Magnus Expansions
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    Chapter 115 Gauss Methods
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    Chapter 116 General Linear Methods
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    Chapter 117 Hamiltonian Systems
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    Chapter 118 Heterogeneous Multiscale Methods for ODEs
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    Chapter 120 Index Concepts for Differential-Algebraic Equations
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    Chapter 121 Initial Value Problems
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    Chapter 122 Lie Group Integrators
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    Chapter 123 Lobatto Methods
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    Chapter 124 Mechanical Systems
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    Chapter 126 Chebyshev Polynomials
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    Chapter 128 Multistep Methods
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    Chapter 129 Nyström Methods
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    Chapter 130 One-Step Methods, Order, Convergence
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    Chapter 132 Order Conditions and Order Barriers
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    Chapter 134 Order Stars and Stability Domains
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    Chapter 135 Oscillatory Problems
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    Chapter 139 Radau Methods
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    Chapter 155 Modeling of Blood Clotting
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    Chapter 156 Distributions and the Fourier Transform
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    Chapter 157 Interferometric Imaging and Time Reversal in Random Media
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    Chapter 158 Inversion Formulas in Inverse Scattering
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    Chapter 161 Computational Mechanics
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    Chapter 162 Angiogenesis, Computational Modeling Perspective
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    Chapter 173 Complexity of Computational Problems in Exact Linear Algebra
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    Chapter 192 Finite Fields
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    Chapter 201 Logical Characterizations of Complexity Classes
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    Chapter 204 Markov Random Fields in Computer Vision: MAP Inference and Learning
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    Chapter 212 Property Testing
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    Chapter 231 Logarithmic Norms
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    Chapter 233 Exact Wavefunctions Properties
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    Chapter 234 Density Functional Theory
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    Chapter 236 Hartree–Fock Type Methods
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    Chapter 237 Post-Hartree-Fock Methods and Excited States Modeling
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    Chapter 238 Linear Time Independent Reaction Diffusion Equations: Computation
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    Chapter 239 Molecular Geometry Optimization, Models
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    Chapter 240 Relativistic Theories for Molecular Models
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    Chapter 241 Relativistic Models for the Electronic Structure of Atoms and Molecules
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    Chapter 242 Classical Iterative Methods
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    Chapter 243 Nuclear Modeling
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    Chapter 245 Numerical Approaches for High-Dimensional PDEs for Quantum Chemistry
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    Chapter 246 Coupled-Cluster Methods
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    Chapter 247 Quantum Monte Carlo Methods in Chemistry
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    Chapter 248 Finite Element Methods for Electronic Structure
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    Chapter 249 Finite Difference Methods in Electronic Structure Calculations
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    Chapter 250 Programming Languages for Scientific Computing
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    Chapter 252 Linear Scaling Methods
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    Chapter 253 Large-Scale Electronic Structure and Nanoscience Calculations
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    Chapter 254 Fast Methods for Large Eigenvalues Problems for Chemistry
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    Chapter 255 A Priori and A Posteriori Error Analysis in Chemistry
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    Chapter 257 Quantum Time-Dependent Problems
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    Chapter 258 Numerical Analysis of Eigenproblems for Electronic Structure Calculations
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    Chapter 260 Born–Oppenheimer Approximation, Adiabatic Limit, and Related Math. Issues
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    Chapter 261 Liquid-Phase Simulation: Theory and Numerics of Hybrid Quantum-Mechanical/Classical Approaches
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    Chapter 262 Mathematical Theory for Quantum Crystals
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    Chapter 265 Calculation of Ensemble Averages
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    Chapter 267 Computation of Free Energy Differences
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    Chapter 269 Quantum Control
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    Chapter 270 Interior Point Methods
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    Chapter 271 Atomistic to Continuum Coupling
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    Chapter 273 Applications to Real Size Biological Systems
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    Chapter 274 Molecular Geometry Optimization: Algorithms
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    Chapter 275 Fitzhugh–Nagumo Equation
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    Chapter 276 Poisson-Nernst-Planck Equation
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    Chapter 277 Mathematical Models for Oil Reservoir Simulation
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    Chapter 279 Large-Scale Computing for Molecular Dynamics Simulation
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    Chapter 280 Convergence Acceleration
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    Chapter 281 Hierarchical Matrices
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    Chapter 282 Discontinous Galerkin Methods: Time-dependent Problems
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    Chapter 283 Computational Complexity
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    Chapter 284 Levin Quadrature
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    Chapter 285 Numerical Analysis
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    Chapter 286 Computational Dynamics
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    Chapter 287 Kinetic Equations: Computation
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    Chapter 292 Computational Partial Differential Equations
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    Chapter 293 Rational Approximation
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    Chapter 294 Bidomain Model: Computation
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    Chapter 295 Greedy Algorithms
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    Chapter 296 Preconditioning
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    Chapter 297 Eikonal Equation: Computation
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    Chapter 298 Gas Dynamics Equations: Computation
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    Chapter 299 Korteweg-de Vries Equation
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    Chapter 300 Numerical Analysis of Fredholm Integral Equations
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    Chapter 301 Machine Learning Algorithms
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    Chapter 303 Integro-Differential Equations: Computation
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    Chapter 304 Dynamic Programming
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    Chapter 306 Radial Basis Functions
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    Chapter 307 Chebyshev Iteration
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    Chapter 309 Bidomain Model: Analytical Properties
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    Chapter 312 Hardware-Oriented Numerics for PDE
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    Chapter 313 Advancing Front Methods
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    Chapter 314 Delaunay Triangulation
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    Chapter 316 Hyperbolic Conservation Laws: Analytical Properties
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    Chapter 317 Bézier Curves and Surfaces
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    Chapter 318 Numerical Steepest Descent
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    Chapter 319 Burgers Equation
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    Chapter 320 Fokker-Planck Equation: Computation
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    Chapter 321 Homotopy Methods
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    Chapter 322 Computational Proofs in Dynamics
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    Chapter 323 Multiphase Flow: Computation
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    Chapter 324 Representation of Floating-Point Numbers
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    Chapter 326 Interval Arithmetics
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    Chapter 327 Bayesian Statistics: Computation
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    Chapter 328 Metropolis Algorithms
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    Chapter 329 Interpolation
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    Chapter 330 Least Squares Finite Element Methods
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    Chapter 331 Polynomial Chaos Expansions
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    Chapter 332 Reproducibility: Methods
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    Chapter 333 Hyperbolic Conservation Laws: Computation
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    Chapter 335 Bidomain Model: Applications
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    Chapter 337 Multigrid Methods: Algebraic
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    Chapter 338 Multigrid Methods: Geometric
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    Chapter 339 Approximation of Manifold-Valued Functions
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    Chapter 340 Fisher’s Equation
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    Chapter 341 Adaptive Mesh Refinement
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    Chapter 342 Matrix Functions: Computation
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    Chapter 345 Hamilton–Jacobi Equations
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    Chapter 347 Phase Plane: Computation
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    Chapter 349 Lattice Boltzmann Methods
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    Chapter 350 hp-Version Finite Element Methods
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    Chapter 353 Conditioning
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    Chapter 354 Gabor Analysis and Algorithms
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    Chapter 355 Fast Fourier Transform
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    Chapter 357 Riemann Problem
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    Chapter 358 Least Squares Calculations
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    Chapter 359 Monte Carlo Integration
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    Chapter 360 Front Tracking
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    Chapter 362 Numerics for the Control of Partial Differential Equations
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    Chapter 364 Hodgkin-Huxley Equations
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    Chapter 365 Boundary Element Methods
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    Chapter 366 Absorbing Boundaries and Layers
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    Chapter 367 Monte Carlo Simulation
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    Chapter 370 Multivariate Approximation
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    Chapter 371 Curvelets
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    Chapter 372 Differentiation: Computation
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    Chapter 373 Inverse Problems: Numerical Methods
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    Chapter 374 Newton-Raphson Method
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    Chapter 377 Minimal Surface Equation
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    Chapter 379 Fast Marching Methods
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    Chapter 382 Diffusion Equation: Computation
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    Chapter 384 Bifurcations: Computation
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    Chapter 385 Multiresolution Methods
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    Chapter 386 Orthogonal Polynomials: Computation
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    Chapter 387 Immersed Interface/Boundary Method
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    Chapter 389 Euler Equations: Computations
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    Chapter 390 Numerical Analysis of Ordinary Differential Equations
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    Chapter 391 Quasi-Monte Carlo Methods
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    Chapter 394 Numerical Homogenization
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    Chapter 395 Filon Quadrature
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    Chapter 396 Belousov–Zhabotinsky Reaction
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    Chapter 398 Calcium Dynamics
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    Chapter 404 Bootstrapping
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    Chapter 405 Boussinesq Equations
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    Chapter 409 Discrete and Continuous Dispersion Relations
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    Chapter 411 Domain Decomposition
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    Chapter 412 Error Estimation and Adaptivity
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    Chapter 414 Finite Difference Methods
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    Chapter 415 Galerkin Methods
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    Chapter 416 Group Velocity Analysis
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    Chapter 419 Linear Programming
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    Chapter 420 Regression
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    Chapter 421 Lyapunov Exponents: Computation
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    Chapter 424 Parallel Computing
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    Chapter 425 Parallel Computing Architectures
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    Chapter 426 Parameter Identification
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    Chapter 432 Geometry Processing
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    Chapter 433 Finite Volume Methods
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    Chapter 435 ADI Methods
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    Chapter 439 Compressive Sensing
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    Chapter 445 Eigenvalues and Eigenvectors: Computation
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    Chapter 448 Fast Multipole Methods
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    Chapter 450 Finite Element Methods
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    Chapter 451 Functional Equations: Computation
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    Chapter 462 Model Reduction
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    Chapter 469 Quadratic Programming
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    Chapter 481 Electro-Mechanical Coupling in Cardiac Tissue
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    Chapter 482 Petrov-Galerkin Methods
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    Chapter 485 Linear Elastostatics
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    Chapter 487 Elastodynamics
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    Chapter 491 Composite Materials and Homogenization
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    Chapter 496 Particulate Composite Media
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    Chapter 503 Compressible Flows
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    Chapter 509 Particulate Flows (Fluid Mechanics)
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    Chapter 510 Dry Particulate Flows
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    Chapter 511 Electromagnetics-Maxwell Equations
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    Chapter 513 Medical Applications in Bone Remodeling, Wound Healing, Tumor Growth, and Cardiovascular Systems
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    Chapter 526 Methods for High-Dimensional Parametric and Stochastic Elliptic PDEs
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    Chapter 527 Analysis and Computation of Hyperbolic PDEs with Random Data
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    Chapter 531 Meshless and Meshfree Methods
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    Chapter 533 Extended Finite Element Method (XFEM)
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    Chapter 538 Global Estimates for hp-Methods
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    Chapter 546 Error Estimates for Linear Hyperbolic Equations
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    Chapter 549 A Posteriori Error Estimates of Quantities of Interest
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    Chapter 554 Discontinous Galerkin Methods: Basic Algorithms
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    Chapter 559 Direct Methods for Linear Algebraic Systems
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    Chapter 560 Multiscale Numerical Methods in Atmospheric Science
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    Chapter 562 Multiscale Multi-cloud Modeling and the Tropics
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    Chapter 563 Framework and Mathematical Strategies for Filtering or Data Assimilation
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    Chapter 567 Algorithms for Low Frequency Climate Response
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    Chapter 571 Information Theory for Climate Change and Prediction
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    Chapter 574 Dynamical Models for Climate Change
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    Chapter 575 Mathematical Methods for Large Geophysical Data Sets
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    Chapter 585 Computational Plasma Physics
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    Chapter 586 Overview of Inverse Problems
Overall attention for this book and its chapters
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (92nd percentile)
  • High Attention Score compared to outputs of the same age and source (97th percentile)

Mentioned by

twitter
27 tweeters
facebook
4 Facebook pages

Citations

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24 Dimensions

Readers on

mendeley
132 Mendeley
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Title
Encyclopedia of Applied and Computational Mathematics
Published by
arXiv, January 2015
DOI 10.1007/978-3-540-70529-1
ISBNs
978-3-54-070528-4, 978-3-54-070529-1, 978-3-54-070530-7, 978-3-66-252872-3
Authors

Matthew G. Knepley

Editors

Björn Engquist

Twitter Demographics

The data shown below were collected from the profiles of 27 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 132 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United Kingdom 1 <1%
Spain 1 <1%
United States 1 <1%
Canada 1 <1%
Unknown 128 97%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 33 25%
Researcher 17 13%
Student > Bachelor 14 11%
Student > Master 11 8%
Professor > Associate Professor 6 5%
Other 22 17%
Unknown 29 22%
Readers by discipline Count As %
Engineering 27 20%
Mathematics 17 13%
Computer Science 9 7%
Biochemistry, Genetics and Molecular Biology 8 6%
Physics and Astronomy 8 6%
Other 23 17%
Unknown 40 30%

Attention Score in Context

This research output has an Altmetric Attention Score of 16. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 28 March 2022.
All research outputs
#1,884,614
of 22,255,188 outputs
Outputs from arXiv
#31,398
of 903,314 outputs
Outputs of similar age
#11,473
of 150,671 outputs
Outputs of similar age from arXiv
#100
of 3,698 outputs
Altmetric has tracked 22,255,188 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 91st percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 903,314 research outputs from this source. They receive a mean Attention Score of 3.9. This one has done particularly well, scoring higher than 96% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 150,671 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 92% of its contemporaries.
We're also able to compare this research output to 3,698 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 97% of its contemporaries.