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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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"Sparse modeling is a rapidly developing area at the intersection of statistical learning and signal processing, motivated by the age-old statistical problem of selecting a small number of predictive variables in high-dimensional datasets. This collection describes key approaches in sparse modeling, focusing on its applications in fields including neuroscience, computational biology, and computer vision. Sparse modeling methods can improve the interpretability of predictive models and aid efficient recovery of high-dimensional unobserved signals from a limited number of measurements. Yet despite significant advances in the field, a number of open issues remain when sparse modeling meets real-life applications. The book discusses a range of practical applications and state-of-the-art approaches for tackling the challenges presented by these applications. Topics considered include the choice of method in genomics applications; analysis of protein mass-spectrometry data; the stability of sparse models in brain imaging applications; sequential testing approaches; algorithmic aspects of sparse recovery; and learning sparse latent models"--MIT CogNet.
Sparse matrices. --- Sampling (Statistics) --- Mathematical models. --- Data reduction. --- Reduction of data --- Automatic data collection systems --- Statistics --- Models, Mathematical --- Simulation methods --- Random sampling --- Statistics of sampling --- Mathematical statistics --- Spare matrix techniques --- Matrices --- COMPUTER SCIENCE/Machine Learning & Neural Networks --- NEUROSCIENCE/General
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This volume describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods challenging some common assumptions and justifications of standard approaches.
Sparse matrices. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Spare matrix techniques --- Matrices --- Sparse matrices
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Sparse matrices --- Data processing --- Addresses, essays, lectures --- -Sparse matrices --- -519.6 --- 681.3*I3 --- Spare matrix techniques --- Matrices --- -Addresses, essays, lectures --- Computational mathematics. Numerical analysis. Computer programming --- Computer graphics (Computing methodologies) --- Sparse matrices. --- Data processing. --- 681.3*I3 Computer graphics (Computing methodologies) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Sparse matrices - Data processing - Addresses, essays, lectures --- Sparse matrices - Addresses, essays, lectures
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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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This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research are available for download at the associated web site.
Transformations (Mathematics) --- Signal processing. --- Image processing. --- Sparse matrices. --- Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Spare matrix techniques --- Matrices --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Algorithms --- Differential invariants --- Geometry, Differential --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing
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Numerical analysis --- Sparse matrices --- data processing --- -519.6 --- 681.3*G13 --- Spare matrix techniques --- Matrices --- Data processing --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Sparse matrices - data processing
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Numerical analysis --- Sparse matrices --- Congresses --- -519.6 --- 681.3*G13 --- Spare matrix techniques --- Matrices --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Sparse matrices - Congresses
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Sparse matrices --- Matrices éparses --- Data processing --- Informatique --- -519.6 --- 681.3*G13 --- Spare matrix techniques --- Matrices --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Data processing. --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Matrices éparses --- 519.6 --- Sparse matrices - Data processing
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Sparse matrices --- Linear systems --- Matrices éparses --- Systèmes linéaires --- 519.61 --- 681.3*G13 --- Numerical methods of algebra --- Numerical linear algebra: conditioning; determinants; eigenvalues and eigenvectors; error analysis; linear systems; matrix inversion; pseudoinverses; singular value decomposition; sparse, structured, and very large systems (direct and iterative methods) --- 519.61 Numerical methods of algebra --- Matrices éparses --- Systèmes linéaires --- Spare matrix techniques --- Matrices --- Systems, Linear --- Differential equations, Linear --- System theory
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