Inverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies.The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are mode…
Historical Introduction: Issai Schur and the Early Development of the Schur Complement -- Basic Properties of the Schur Complement -- Eigenvalue and Singular Value Inequalities of Schur Complements -- Block Matrix Techniques -- Closure Properties -- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach -- Schur complements in statistics and probability -- Schur Complements and …
Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media -- Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator -- Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc -- On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type -- Fourier Integral Operators and Gelfand-Shilov Spac…
to Quantum Trajectories -- The Bohmian Route to the Hydrodynamic Equations -- The Phase Space Route to the Hydrodynamic Equations -- The Dynamics and Properties of Quantum Trajectories -- Function and Derivative Approximation on Unstructured Grids -- Applications of the Quantum Trajectory Method -- Adaptive Methods for Trajectory Dynamics -- Quantum Trajectories for Multidimensional Dynamics --…
What is a Quadrature Domain? -- Recent Progress and Open Problems in the Bergman Space -- The Bergman Kernel and Quadrature Domains in the Plane -- The Cauchy Transform -- Quadrature Domains and Fluid Dynamics -- On Uniformly Discrete Sequences in the Disk -- Algebraic Aspects of the Dirichlet Problem -- Linear Analysis of Quadrature Domains. IV -- Restriction, Localization and Microlocalizatio…
Surveys -- An Introduction to Lattice Chiral Fermions -- Computing f(A)b for Matrix Functions f -- Computational Methods for the Fermion Determinant and the Link Between Overlap and Domain Wall Fermions -- Monte Carlo Simulations of Lattice QCD -- Lattice QCD -- Determinant and Order Statistics -- Monte Carlo Overrelaxation for SU(N) Gauge Theories -- Improved Staggered Fermions -- Perturbative…
Contents -- General Preface -- Labels and Abbreviations -- Chapter I. Systems of Linear Algebraic Equations -- Chapter II. Systems of Linear Algebraic Equations -- Chapter III. Linear Integral Equations -- References -- Application -- Index -- Glossary of Symbols.This book presents the author’s new method of two-stage maximization of likelihood function, which helps to solve a series of non-s…
Invited Lectures -- Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications -- A General Frame for the Construction of Constrained Curves -- DMBVP for Tension Splines -- Robust Numerical Methods for the Singularly Perturbed Black-Scholes Equation -- Contributed Lectures -- On Certain Properties of Spaces of Locally Sobolev Functions -- On Some Properties of Hom…
Line Search Descent Methods for Unconstrained Minimization -- Standard Methods for Constrained Optimization -- New Gradient-Based Trajectory and Approximation Methods -- Example Problems -- Some Theorems.This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form without neglecting rigour. The work should enable the prof…
Preliminaries -- Elements of Convex Analysis, Duality Theory -- A Posteriori Error Analysis for Idealizations in Linear Problems -- A Posteriori Error Analysis for Linearizations -- A Posteriori Error Analysis for Some Numerical Procedures -- Error Analysis for Variational Inequalities of the Second Kind.This volume provides a posteriori error analysis for mathematical idealizations in modeling…