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 20 of 21 for “"Numerical linear Algebra"”.
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The power of randomized algorithms : from numerical linear algebra to biological systems
… to accelerate the solution of core problems in numerical linear algebra. In particular, we give a randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving upon what is possible with traditional deterministic methods. We …
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Techniques for the Interactive Development of Numerical Linear Algebra Libraries for Scientific Computation
The development of high-performance numerical algorithms and their effective use in application codes is an iterative process involving the refinement of the algorithms and their implementations that continues during the lifetime of the algorithm. Knowledge and expertise from the areas of numerical …
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Jacobi-type methods on semisimple Lie algebras : a Lie algebraic approach to numerical linear algebra
Es wird eine Lie-algebraische Verallgemeinerung sowohl des klassischen als auch des Sortier-Jacobi-Verfahrens für das symmetrische Eigenwertproblem behandelt. Der koordinatenfreie Zugang ermöglicht durch eine neue Betrachtungsweise die Vereinheitlichung strukturierter Eigen- und …
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Sparse approximations, iterative methods, and faster algorithms for matrices and graphs
… faster algorithms for a host of core problems in numerical linear algebra and graph algorithms. The resulting insights often lead to first in decades progress on the studied problems.
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Fast spectral primitives for directed graphs
… we study several algorithmic problems involving numerical linear algebra, probability, and statistics. Its main results include the following: -- We give the first nearly linear time algorithms for a large class of directed graph problems including computing the stationary distribution of a …
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APPROXIMATE GROBNER BASES A BACKWARDS APPROACH
… object of exact computation polynomial algebra, as it answers many of the important questions of commutative algebra, such as ideal membership and computation of the Hilbert polynomial. It is traditionally computed using variants of Buchberger’s algorithm. Here, we take a backwards …
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Towards Efficient and Scalable Electronic Structure Methods for the Treatment of Relativistic Effects and Molecular Response
… of molecular response is cast into a large numerical linear algebra problem suitable for modern high--performance computing architectures. This chapter outlines a highly scalable method which allows for rapid evaluation of response functions in a reduced dimension.
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Model reduction for Hidden Markov models
… finite alphabet Hidden Markov Models and Jump Linear Systems with finite parameter space. The reduction algorithms employ convex optimization and numerical linear algebra tools and do not pose any structural requirements on the systems at hand. In the Jump Linear Systems case, a distance metric …
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Faster algorithms for convex and combinatorial optimization
… on convex and combinatorial optimization: --Linear Programming: We obtain the first improvement to the running time for linear programming in 25 years. The convergence rate of this randomized algorithm nearly matches the universal barrier for interior point methods. As a corollary, we obtain …
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Probabilistic Approximations of Matrix Decompositions for Inverse Problems
… Much of the analysis in this thesis is of linear inverse problems with Gaussian unknowns. Such problems can be expressed in terms of linear algebra, so much of this thesis is concerned with numerical linear algebra. A particular focus is approximate matrix decompositions. This thesis makes …
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Continuous low-rank tensor decompositions, with applications to stochastic optimal control and data assimilation
… provides a natural framework for building numerical algorithms that effectively, naturally, and automatically adapt to problem structure. The first part of this thesis describes a compressed continuous computation framework centered around a continuous analogue to the (discrete) …
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Analytic and Numerical aspects of isospectral flows
In this thesis we address the analytic and numerical aspects of isospectral flows. Such flows occur in mathematical physics and numerical linear algebra. Their main structural feature is to retain the eigenvalues in the solution space. We explore the solution of Isospectral flows and their …
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Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations
<p>Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the "Big Data" era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing …
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Dimension Reduction in Structured Dynamical Systems: Optimal-𝓗<sub>2</sub> Approximation, Data-Driven Balancing, and Real-Time Monitoring
… methods for system-theoretic model reduction of linear time-invariant systems are considered. We generalize conditions for which the balanced truncation $mathcal{H}_{infty}$ error bound is known to hold with equality. Specifically, we show that the bound is tight for single-input, single-output …
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Diagonal Estimation with Probing Methods
… choices in their construction, and conclude with numerical results on diagonal estimation and ordering problems, demonstrating the strengths of our newly-developed methods alongside existing methods.
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Algorithmic advances in learning from large dimensional matrices and scientific data
… first of the three parts of this thesis explores numerical linear algebra tools to develop efficient algorithms for machine learning with reduced computation cost and improved scalability. Here, we first develop inexpensive algorithms combining various ideas from linear algebra and approximation …
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Uncertainty quantification in ocean state estimation
… due to the large dimensionality of this nonlinear estimation problem and the number of uncertain variables involved. The “Estimating the Circulation and Climate of the Oceans” (ECCO) consortium has developed a scalable system for dynamically consistent estimation of global time-evolving …
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The proxy point method for rank-structured matrices
… the study and application of a hybrid analytic-algebraic compression method, called \textit{the proxy point method}. This work uncovers the full strength of this presently underutilized method that could potentially resolve the above bottleneck for all rank-structured matrix techniques. As a …
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Computation of Approximate Border Bases and Applications
This thesis addresses some of the algorithmic and numerical challenges associated with the computation of approximate border bases, a generalisation of border bases, in the context of the oil and gas industry. The concept of approximate border bases was introduced by D. Heldt, M. Kreuzer, S. …
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Uncertainty Quantification in ocean state estimation
… due to the large dimensionality of this nonlinear estimation problem and the number of uncertain variables involved. The "Estimating the Circulation and Climate of the Oceans" (ECCO) consortium has developed a scalable system for dynamically consistent estimation of global time-evolving …
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