2,567 research outputs found
Deterministic Sampling of Sparse Trigonometric Polynomials
One can recover sparse multivariate trigonometric polynomials from few
randomly taken samples with high probability (as shown by Kunis and Rauhut). We
give a deterministic sampling of multivariate trigonometric polynomials
inspired by Weil's exponential sum. Our sampling can produce a deterministic
matrix satisfying the statistical restricted isometry property, and also nearly
optimal Grassmannian frames. We show that one can exactly reconstruct every
-sparse multivariate trigonometric polynomial with fixed degree and of
length from the determinant sampling , using the orthogonal matching
pursuit, and # X is a prime number greater than . This result is
almost optimal within the factor. The simulations show that the
deterministic sampling can offer reconstruction performance similar to the
random sampling.Comment: 9 page
Discrete schemes for Gaussian curvature and their convergence
In this paper, several discrete schemes for Gaussian curvature are surveyed.
The convergence property of a modified discrete scheme for the Gaussian
curvature is considered. Furthermore, a new discrete scheme for Gaussian
curvature is resented. We prove that the new scheme converges at the regular
vertex with valence not less than 5. By constructing a counterexample, we also
show that it is impossible for building a discrete scheme for Gaussian
curvature which converges over the regular vertex with valence 4. Finally,
asymptotic errors of several discrete scheme for Gaussian curvature are
compared
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