Algorithms for Large Scale Linear Algebraic Systems:: Applications in Science and Engineering - NATO Science Series C 1998 edition

Marc Notes: Proceedings of the NATO Advanced Study Institute on Algorithms for Large Scale Linear Algebraic Systems: State of the Art and Applications in Science and Engineering, Gran Canaria, Spain, June 23-July 6, 1996--T.p. verso.; Includes index.; Published in cooperation with NATO Scientific Affairs Division.. Table of Contents: Preface. Computational Complexity of Solving Large Sparse and Large Special Linear Systems of Equations; V. Y. Pan. Block Iterative Methods for Reduced Systems of Linear Equations; D. J. Evans. Parallel Implicit Schemes for the Solution of Linear Systems; D. J. Evans. Adaptive Multigrid Methods for Hybrid Finite Elements; L. Ferragut. On Finding and Analyzing the Structure of The Cholesky Factor; A. George. The Go-Away Algorithm for Block Factorization of a Sparse Matrix; P. R. Almeida, J. R. Franco. Renumbering Sparse Matrices by Simulated Annealing; G. Winter, et al. Preconditioned Krylov Subspace Methods; Y. Saad. Preconditioning Krylov Methods; A. Suarez, et al. Convergence and Numerical Behaviour of the Krylov Space Methods; Z. Strakos. Look-ahead Block-CG Algorithms; C. G. Broyden. Iterative Bi-CG Type Methods and Implementation Aspects; H. Van der Vorst, G. L. G. Sleijpen. Problems of Breakdown and Near-Breakdown in Lanczos-Based Algorithms; C. Brezinski, et al. Hybrid Methods for Solving Systems of Equations; C. Brezinski. ABS Algorithms for Linear Equations and Applications to Optimization; E. Spedicato, et al. Solving Inverse Thermal Problems Using Krylov Methods; G. Montero. An Introduction on Global Optimization by Genetic Algorithms; G. Winter, et al. Blackbox and Non-blackbox Optimization: A Common Perspective; H. Kargupta. Messy Genetic Algorithms: Recent Developments; H. Kargupta. List of Contributors. Index."Publisher Marketing: An overview of the most successful algorithms and techniques for solving large, sparse systems of equations and some algorithms and strategies for solving optimization problems. The most important topics dealt with concern iterative methods, especially Krylov methods, ordering techniques, and some iterative optimization tools. The book is a compendium of theoretical and numerical methods for solving large algebraic systems, special emphasis being placed on convergence and numerical behaviour as affected by rounding errors, accuracy in computing solutions for ill-conditioned matrices, preconditioning effectiveness, ordering procedures, stability factors, hybrid procedures and stopping criteria. Recent advances in numerical matrix calculations are presented, especially methods to accelerate the solution of symmetric and unsymmetric linear systems. Convergence analysis of the multi-grid method using a posteriori error estimation in second order elliptic equations are presented. Some inverse problems are also included. Evolution based software is described, such as genetic algorithms and evolution strategies, relations and class hierarchising to improve the exploration of large search spaces and finding near-global optima. Recent developments in messy genetic algorithms are also described. The tutorial nature of the book makes it suitable for mathematicians, computer scientists, engineers and postgraduates.

Contributor Bio:  North Atlantic Treaty Organization Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index