The QR Algorithm -- The QZ Algorithm -- The Krylov-Schur Algorithm -- Structured Eigenvalue Problems -- Background in Control Theory Structured Eigenvalue Problems -- Software.The purpose of this book is to describe recent developments in solving eig- value problems, in particular with respect to the QR and QZ algorithms as well as structured matrices. Outline Mathematically speaking, the eigen…
Preliminary general material -- Steady-State Problems -- Pseudomonotone or weakly continuous mappings -- Accretive mappings -- Potential problems: smooth case -- Nonsmooth problems; variational inequalities -- Systems of equations: particular examples -- Evolution Problems -- Special auxiliary tools -- Evolution by pseudomonotone or weakly continuous mappings -- Evolution governed by accretive …
Portfolio Optimization -- One-Variable Optimization -- Optimal Portfolios with N Assets -- Unconstrained Optimization in N Variables -- The Steepest Descent Method -- The Newton Method -- Quasi-Newton Methods -- Conjugate Gradient Methods -- Optimal Portfolios with Restrictions -- Larger-Scale Portfolios -- Data-Fitting & The Gauss-Newton Method -- Equality Constrained Optimization -- Linear Eq…
Bounded Imaginary Powers and H?-Calculus of the Stokes Operator in Unbounded Domains -- Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point -- Well-posedness of a Two-phase Flow with Soluble Surfactant -- Resolvent Differences for General Obstacles -- Special Finite Time Extinction in …
Atomistic Models -- Lattice Gas Models and Kinetic Monte Carlo Simulations of Epitaxial Growth -- Cluster Diffusion and Island Formation on fcc(111) Metal Surfaces Studied by Atomic Scale Computer Simulations -- A Multiscale Study of the Epitaxial CVD of Si from Chlorosilanes -- Off-lattice Kinetic Monte Carlo Simulations of Strained Heteroepitaxial Growth -- Quasicontinuum Monte Carlo Simulati…
Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales -- Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions -- Adaptive Monte Carlo Algorithms for Stopped Diffusion -- The Heterogeneous Multi-Scale Method for Homogenization Problems -- A Coarsening Multigrid Method for Flow in Heterogeneous Porous Media -- On th…
Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications -- Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction -- Computational Techniques for the Verification and Control of Hybrid Systems -- Data Assimilation Methods for an Oceanographic Problem -- Ant Colonies: a Nature inspired Paradigm for the Mathematical Modelling of Self-Organizi…
Gas Flows -- Governing Equations and Slip Models -- Shear-Driven Flows -- Pressure-Driven Flows -- Thermal Effects in Microscales -- Prototype Applications of Gas Flows -- Basic Concepts and Technologies -- Liquid Flows -- Electrokinetic Flows -- Surface Tension-Driven Flows -- Mixers and Chaotic Advection -- Simple Fluids in Nanochannels -- Water in Nanochannels -- Electroosmotic Flow in Nanoc…
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
A Particle Strategy for Solving the Fokker-Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions -- Extended Meshfree Method for Elastic and Inelastic Media -- Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations -- The ?-shape Based Natural Element Method in Solid and Fluid Mechanics -- A Particle…