Abstract | ||
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Sparse interpolation from at least 2n uniformly spaced interpolation points tj can be traced back to the exponential fitting method
[MATH HERE]
of de Prony from the 18-th century [5]. Almost 200 years later this basic problem is also reformulated as a generalized eigenvalue problem [8]. We generalize (1) to sparse interpolation problems of the form
[MATH HERE]
and some multivariate formulations thereof, from corresponding regular interpolation point patterns. Concurrently we introduce the wavelet inspired paradigm of dilation and translation for the analysis (2) of these complex-valued structured univariate or multivariate samples. The new method is the result of a search on how to solve ambiguity problems in exponential analysis, such as aliasing which arises from too coarsely sampled data, or collisions which may occur when handling projected data.
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Year | DOI | Venue |
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2018 | 10.1145/3313880.3313887 | ACM Communications in Computer Algebra |
Field | DocType | Volume |
Discrete mathematics,Algebra,Sparse interpolation,Mathematics | Journal | 52 |
Issue | ISSN | Citations |
3 | 1932-2240 | 0 |
PageRank | References | Authors |
0.34 | 5 | 2 |
Name | Order | Citations | PageRank |
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Annie Cuyt | 1 | 161 | 41.48 |
Wen-shin Lee | 2 | 182 | 15.67 |