Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 19 of 19 for “"Singular vectors"”.
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An Examination into the Statistics of the Singular Vectors for the Multi-User MIMO Wireless Channel
… (MIMO) wireless channels make use of the singular value decomposition (SVD) of the channel matrix. For the multi-user case, the SVD of the channel matrix for each user may result in right and left singular vectors that are similar between users. This proposes another descriptive …
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A study of local approximations in information theory
… existing literature has demonstrated that the singular vectors of additive white Gaussian noise channels are Hermite polynomials, and the singular vectors of Poisson channels are Laguerre polynomials. We characterize the set of infinite alphabet channels whose singular value decompositions …
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Ensemble regression : using ensemble model output for atmospheric dynamics and prediction
… ER performed in the subspace of the leading PV singular vectors. Secondly, using the example of the lagged sensitivity of tropical cyclone tracks to preexisting midtropospheric heights, ER is used to infer dynamical relationships from statistical sensitivities, to identify, in real-time, the …
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On Vertex Operator Algebras of Affine Type at Admissible Levels
… this, it is crucial to obtain knowledge of the singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. We study in particular the simple VOAs associated to …
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Message Passing Algorithms for Statistical Estimation and Communication
… *n*<sub>2</sub> low-rank matrix with *k*-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular vectors with high probability, with sample- and time-complexity both depending only on *k* and not on …
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Distributed Singular Value Decomposition Through Least Squares
Singular value decomposition (SVD) is an essential matrix factorization technique that decomposes a matrix into singular values and corresponding singular vectors that form orthonormal bases. SVD has wide-ranging applications from principal component analysis (PCA) to matrix completion and …
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Fréchet Sensitivity Analysis and Parameter Estimation in Groundwater Flow Models
… operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant …
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Incremental proper orthogonal decomposition for PDE simulation data: Algorithms and analysis
… to bound the error in the incrementally computed singular values and singular vectors. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers' equation, a 1D FitzHugh-Nagumo PDE system, and a 2D Navier-Stokes problem"--Abstract, page iv.</p>
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Multiprocessor sparse SVD algorithms and applications
… develop four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly consider the SVD of unstructured sparse matrices in which the number of rows may be substantially larger or smaller than the number of …
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Interannual middle-latitude atmosphere-ocean interactions
… This is the same balance as the "neutral vectors" described by Marshall and Molteni (1993). Neutral vectors are the right singular vectors of the linearized atmospheric model's tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest response …
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On the origins of the ice ages : insolation forcing, age models, and nonlinear climate change
… represent the spatial modes of variability and singular vectors to represent seasonal and long-term changes. The leading four spatial and temporal modes describe over 99% of the insolation variability making this a relatively simple and compact description of the full insolation forcing. …
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Reduced rank filtering in chaotic systems with application in geophysical sciences
… of uncertainty, which translate to the leading singular vectors of the state transition matrix over the forecast period, so long as the linear approximation of the dynamics is valid.
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An Implementation-Based Exploration of HAPOD: Hierarchical Approximate Proper Orthogonal Decomposition
… of nonlinear PDEs. The POD requires the left singular vectors from the singular value decomposition (SVD) of an n-by-m "snapshot matrix" S, each column of which represents the computed state of the system at a given time. However, the direct computation of this decomposition can be …
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Large-Scale Simulations Using First and Second Order Adjoints with Applications in Data Assimilation
… uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order …
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Nonlinear filtering of high dimensional, chaotic, multiple timescale correlated systems
… filtering. We introduce the idea of future right-singular vectors to produce projection operators, enabling assimilation in a lower dimensional subspace. We show that particle filtering algorithms using dynamically generator projection operators, in particular the future right-singular vectors, …
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Reduced order modeling of convection-dominated flows, dimensionality reduction and stabilization
… at the algebraic level, using left and right singular vectors of the reduced system matrices. The proposed stabilization method is general and applicable to a large variety of linear time-varying ROMs.
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Techniques to account for and reduce model inadequacy in ensemble-based filters
… sensitivity which is obtained using parametric singular vectors. It is found that PVM is able to estimate the correct state-dependent model error structure if the parametric vectors are constructed over an optimization time (T0p) which is equal to the state-dependent optimal time (Tm). The …
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Matrix probing, skeleton decompositions, and sparse Fourier transform
… in accurate skeleton decompositions. When the singular vectors (or more generally the generating vectors) are incoherent, we show that a simple algorithm returns an accurate skeleton in sublinear O(l3) time from l ~/- k logn rows and columns drawn uniformly at random, with an approximation …
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Algorithms and algorithmic obstacles for probabilistic combinatorial structures
… our algorithm is two new steps of thresholding singular values and rescaling singular vectors in the application of the "vanilla" alternating minimization algorithm. The structure of sparse random regular graphs is used heavily for controlling the impact of these regularization steps.