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Simultaneous localization and mapping (SLAM) is a process where an autonomous vehicle builds a map of an unknown environment while concurrently generating an estimate for its location. This book is concerned with computationally efficient solutions to the large scale SLAM problems using exactly sparse Extended Information Filters (EIF). The invaluable book also provides a comprehensive theoretical analysis of the properties of the information matrix in EIF-based algorithms for SLAM. Three exactly sparse information filters for SLAM are described in detail, together with two efficient and exact methods for recovering the state vector and the covariance matrix. Proposed algorithms are extensively evaluated both in simulation and through experiments.

Mobile robots. --- Robots --- Sparse matrices. --- Robotics. --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Automation --- Machine theory --- Spare matrix techniques --- Matrices --- Robot control --- Robotics --- Control systems.

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This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.

Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Sparse matrices --- Spare matrix techniques --- Matrices --- Conferences - Meetings --- Numerical analysis --- Sparse grids. --- Mathematics. --- Algorithms. --- Computer mathematics. --- Computational Science and Engineering. --- Algorithm Analysis and Problem Complexity. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Grids, Sparse --- Discretization (Mathematics) --- Numerical grid generation (Numerical analysis) --- Foundations --- Computer science. --- Computer software. --- Informatics --- Software, Computer --- Computer systems

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Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.

Matrices --- Differential equations --- Iterative methods (Mathematics) --- Integral equations --- Sparse matrices --- Equations différentielles --- Itération (Mathématiques) --- Equations intégrales --- Matrices éparses --- Numerical solutions --- Data processing --- Solutions numériques --- Informatique --- data processing --- Spare matrix techniques --- Equations, Integral --- Functional equations --- Functional analysis --- Iteration (Mathematics) --- Numerical analysis --- Data processing. --- 517.91 Differential equations --- Equations différentielles --- Itération (Mathématiques) --- Equations intégrales --- Matrices éparses --- Solutions numériques --- 517.91 --- Numerical solutions&delete& --- Sparse matrices - data processing --- Differential equations - Numerical solutions - Data processing --- Iterative methods (Mathematics) - Data processing --- Integral equations - Numerical solutions - Data processing

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This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at  ICM 2010.

Combinatorial analysis. --- Computational complexity. --- Linear systems. --- Sparse matrices. --- Sparse matrices --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Combinatorics --- Spare matrix techniques --- Mathematics. --- Algorithms. --- Computer science --- Convex geometry. --- Discrete geometry. --- Mathematical logic. --- Combinatorics. --- Discrete Mathematics in Computer Science. --- Convex and Discrete Geometry. --- Mathematical Logic and Foundations. --- Algorithm Analysis and Problem Complexity. --- Mathematical analysis --- Matrices --- Discrete groups. --- Logic, Symbolic and mathematical. --- Computer software. --- Software, Computer --- Computer systems --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Groups, Discrete --- Infinite groups --- Complexity, Computational --- Electronic data processing --- Machine theory --- Discrete mathematics --- Computer science—Mathematics. --- Convex geometry . --- Algorism --- Arithmetic --- Geometry --- Combinatorial geometry --- Foundations

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This book provides a view of low-rank and sparse computing, especially approximation, recovery, representation, scaling, coding, embedding, and learning among unconstrained visual data. Included in the book are chapters covering multiple emerging topics in this new field. The text links multiple popular research fields in Human-Centered Computing, Social Media, Image Classification, Pattern Recognition, Computer Vision, Big Data, and Human-Computer Interaction. This book contains an overview of the low-rank and sparse modeling techniques for visual analysis by examining both theoretical analysis and real-world applications. ·         Covers the most state-of-the-art topics of sparse and low-rank modeling ·         Examines the theory of sparse and low-rank analysis to the real-world practice of sparse and low-rank analysis ·         Contributions from top experts voicing their unique perspectives included throughout.

Information visualization. --- Visualization. --- Visual perception. --- Sparse matrices. --- Representations of groups. --- Mathematical models. --- Machine learning. --- Learning, Machine --- Artificial intelligence --- Machine theory --- Models, Mathematical --- Simulation methods --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Optics, Psychological --- Vision --- Perception --- Visual discrimination --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Data visualization --- Visualization of information --- Information science --- Visual analytics --- Spare matrix techniques --- Matrices --- Psychological aspects --- Computer vision. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Machine vision --- Vision, Computer --- Image processing --- Pattern recognition systems --- Optical data processing. --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment