S
Stephen J. Dilworth
Researcher at University of South Carolina
Publications - 120
Citations - 1650
Stephen J. Dilworth is an academic researcher from University of South Carolina. The author has contributed to research in topics: Banach space & Basis (linear algebra). The author has an hindex of 20, co-authored 115 publications receiving 1426 citations. Previous affiliations of Stephen J. Dilworth include University of Texas at Austin & University of Cambridge.
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Explicit constructions of RIP matrices and related problems
TL;DR: In this paper, a new explicit construction of n×N matrices satisfying the Restricted Isometry Property (RIP) was given, which overcomes the natural barrier k=O(n1/2) for proofs based on small coherence, which was used in all previous explicit constructions of RIP matrices.
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The Thresholding Greedy Algorithm, Greedy Bases, and Duality
TL;DR: Some new conditions that arise naturally in the study of the Thresholding Greedy Algorithm are introduced for bases of Banach spaces and a complete duality theory for greedy bases is obtained.
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On the existence of almost greedy bases in Banach spaces
TL;DR: In this article, the authors consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the thresholding greedy algorithm and show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation.
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Coefficient quantization for frames in Banach spaces
TL;DR: In this paper, the problem of approximating linear combinations of elements of a Banach system by linear combinations using quantized coefficients is considered. But the model for this situation will be frames in Banach spaces.
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Approximate Isometries on Finite-Dimensional Normed Spaces
TL;DR: In this article, it was shown that every e-isometry between real normed spaces of the same finite dimension which maps the origin to the origin may be uniformly approximated to within 2e by a linear isometry.