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Iterative methods (Mathematics)

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This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejér property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.

Iterative methods (Mathematics) --- Numerical analysis. --- Mathematical analysis --- Iteration (Mathematics) --- Numerical analysis --- Ill-posed Problems. --- Iteration Method. --- Noisy Data. --- Nonlinear Equations. --- Optimization.

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This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective. Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms. The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented. Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book.

Algorithms. --- Conjugate gradient methods. --- Mathematical optimization. --- Conjugate gradient methods --- Algorithms --- Mathematical optimization --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Mathematical Theory --- Operations Research --- Algebra --- Calculus --- Algorism --- Gradient methods, Conjugate --- Mathematics. --- Operations research. --- Decision making. --- Calculus of variations. --- Quality control. --- Reliability. --- Industrial safety. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Quality Control, Reliability, Safety and Risk. --- Arithmetic --- Approximation theory --- Equations --- Iterative methods (Mathematics) --- Foundations --- Numerical solutions --- System safety. --- Operations Research/Decision Theory. --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Systems engineering --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Prevention --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Reliability (Engineering) --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Isoperimetrical problems --- Variations, Calculus of --- Decision making