Related papers: Parallel sparse interpolation using small primes
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is presented. The proposed approach revises and extends the…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a…
A distinguishing feature of certain intractable problems in prime number theory is the sparsity of the underlying sequence. Motivated by the general problem of finding primes in sparse polynomial sequences, we give an estimate for the…
The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…
Lottery tickets (LTs) is able to discover accurate and sparse subnetworks that could be trained in isolation to match the performance of dense networks. Ensemble, in parallel, is one of the oldest time-proven tricks in machine learning to…
Iterative magnitude pruning methods (IMPs), proven to be successful in reducing the number of insignificant nodes in over-parameterized deep neural networks (DNNs), have been getting an enormous amount of attention with the rapid deployment…
In this paper, we propose a new super resolution technique based on the interpolation followed by registering them using iterative back projection (IBP). Low resolution images are being interpolated and then the interpolated images are…
Microplastics (MPs) are ubiquitous in all ecosystems, affecting wildlife and, ultimately, human health. The complexity of natural samples plus the unspecificity of their treatments to isolate polymers renders the characterization of…
In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has…
We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the…
Sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication beyond memory capacity by implementing sparse…