1. On the size of incoherent systems
- Author
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Nelson, J.L. and Temlyakov, V.N.
- Subjects
- *
PARAMETER estimation , *ALGORITHMS , *MATRICES (Mathematics) , *MATHEMATICS , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
Abstract: This paper concerns systems with small coherence parameter. Simple greedy-type algorithms perform well on these systems, which are also useful in the construction of compressed sensing matrices. We discuss the following problems for both and . How large can a dictionary be, if we prescribe the coherence parameter? How small could the resulting coherence parameter be, if we impose a size on the dictionary? How could we construct such a system? Several fundamental results from different areas of mathematics shed light on these important problems with far-reaching implications in approximation theory. [Copyright &y& Elsevier]
- Published
- 2011
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