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Visar resultat 1 - 5 av 13 avhandlingar som matchar ovanstående sökkriterier.

1. 1. Non-Convex Methods for Compressed Sensing and Low-Rank Matrix Problems

   Författare :Daniele Gerosa; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; compressed sensing; Low-rank Approximation; phase retrieval; Non-convex optimization;

   Sammanfattning : In this thesis we study functionals of the type \( \mathcal{K}_{f,A,\b}(\x)= \mathcal{Q}(f)(\x) + \|A\x - \b \| ^2 \), where \(A\) is a linear map, \(\b\) a measurements vector and \( \mathcal{Q} \) is a functional transform called \emph{quadratic envelope}; this object is a very close relative of the \emph{Lasry-Lions envelope} and its use is meant to regularize the functionals \(f\). Carlsson and Olsson investigated in earlier works the connections between the functionals \( \mathcal{K}_{f,A,\b}\) and their unregularized counterparts \(f(\x) + \|A\x - \b \| ^2 \). LÄS MER

3. 2. Rank Reduction with Convex Constraints

   Författare :Christian Grussler; Institutionen för reglerteknik; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; low-rank approximation; model reduction; non-convex optimization; Douglas-Rachford; matrix completion; overlapping norm; k-support norm; atomic norm;

   Sammanfattning : This thesis addresses problems which require low-rank solutions under convex constraints. In particular, the focus lies on model reduction of positive systems, as well as finite dimensional optimization problems that are convex, apart from a low-rank constraint. LÄS MER

4. 3. Numerical Methods for Wave Propagation : Analysis and Applications in Quantum Dynamics

   Författare :Emil Kieri; Sverker Holmgren; Vasile Gradinaru; Hans O. Karlsson; Tobias Jahnke; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computational wave propagation; quantum dynamics; time-dependent Schrödinger equation; spectral methods; Gaussian beams; splitting methods; low-rank approximation; Scientific Computing; Beräkningsvetenskap;

   Sammanfattning : We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. LÄS MER

5. 4. Robust Estimation of Motion Parameters and Scene Geometry : Minimal Solvers and Convexification of Regularisers for Low-Rank Approximation

   Författare :Marcus Valtonen Örnhag; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Computer Vision; Visual Odometry; Simultaneous Localization and Mapping; minimal solvers; Convex relaxations; Structure from motion;

   Sammanfattning : In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. LÄS MER

7. 5. Algorithms in data mining using matrix and tensor methods

   Författare :Berkant Savas; Lars Eldén; Lieven De Lathauwer; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Volume; Minimization criterion; Determinant; Rank deficient matrix; Reduced rank regression; System identification; Rank reduction; Volume minimization; General algorithm; Handwritten digit classification; Tensors; Higher order singular value decomposition; Tensor approximation; Least squares; Tucker model; Multilinear algebra; Notation; Contraction; Tensor matricization; Newton s method; Grassmann manifolds; Product manifolds; Quasi-Newton algorithms; BFGS and L-BFGS; Symmetric tensor approximation; Local intrinsic coordinates; Global embedded coordinates; ; Numerical analysis; Numerisk analys;

   Sammanfattning : In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. LÄS MER