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 10 of 10 for “"Structured Matrices."”.
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Subcubic Min-Plus Product of Structured Matrices
… for APSP. The Min-Plus product of two 𝑛 × 𝑛 matrices is known to be equivalent to APSP, where the optimal running times of the two problems differ by at most a constant factor. A natural way to approach understanding the complexity of APSP is thus understanding what structure (if any) is …
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Dimensionality reduction for sparse and structured matrices
… case of dimensionality reduction for sparse and structured data. In contrast to popular structure-agnostic methods like Johnson-Lindenstrauss projection and PCA, we seek data compression techniques that take advantage of structure to generate smaller or more powerful compressions. Additionally, …
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The proxy point method for rank-structured matrices
Rank-structured matrix representations, e.g., $\mathcal{H}^2$ and HSS, are commonly used to reduce computation and storage cost for dense matrices defined by interactions between many bodies. The main bottleneck for their application is the expensive computation required to represent a matrix in a …
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Spectrum of some regular graphs with widely spaced modifications
… modifications on the spectrum of some type of structured matrices. We show that by applying those modifications, new eigenvectors that are localized near the components that correspond to the modified rows appear. By knowing the approximate form of those eigenvectors, we also determine a very …
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Linear Algebra, Random Matrices and Lie Theory
… The generalized Cartan decomposition applied to structured matrices proves the existence of several known matrix factorizations at once and at the same time reveals a number of new matrix factorizations. Finally in the last part we derive the joint eigenvalue-like densities of the classical …
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Structured linear algebra problems and applications to system identification
… stability, rank estimation and conditioning for structured matrices. The ideas are developed with attention to potential applications in control and signal processing where such matrices arise routinely. A stability result for the factorization of the broad class of positive definite …
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Efficient machine learning: models and accelerations
… attracts our attention. We introduce the structured matrices based neural network to address this problem. Circulant matrix is one of the structured matrices, where a matrix can be represented using a single vector, so that the matrix is compressed. We further investigate a more flexible …
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Language Evolution for Parallel and Scientific Computing
… mathematical objects such as dense, sparse and structured matrices. These abstractions should enable code reuse for differentiable programming, to enable integration of techniques like sensitivity analysis and scientific machine learning. With the right methodology, these abstractions can …
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Algorithms and software for efficient tensor decompositions
Tensors, which generalize vectors and matrices to higher dimensions, provide a powerful framework for representing and analyzing multi-way data arising in science and engineering. Their ability to capture complex, multi-relational structures makes them invaluable in applications ranging from …
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APPROXIMATE GROBNER BASES A BACKWARDS APPROACH
… the one from which we began, we make avid use of structured (numerical) linear algebra. Additionally, we introduce approximate leading terms and an approximate reduced row echelon form. Neither of these require Gaussian elimination, unlike the exact case.