Related papers: Sparse Interpolation in Terms of Multivariate Cheb…
Chebychev approximations are given for the Gamma and the Polygamma functions in only one contiguous intervall [1..inf] with a definable maximal relative error. The approximations need about three coefficients per decimal until a checked…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…
Most rational systems can be described in terms of orthonormal basis functions. This paper considers the reconstruction of a sparse coefficient vector for a rational transfer function under a pair of orthonormal rational function bases and…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\phi(x)$, called an…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's…
We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a set of solutions to a sparse system is complete. These…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…