Related papers: Revisit Sparse Polynomial Interpolation based on R…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
A novel algorithm is proposed for the interpolation step of the Guruswami-Sudan list decoding algorithm. The proposed method is based on the binary exponentiation algorithm, and can be considered as an extension of the Lee-O'Sullivan…
For the last almost three decades, since the famous Buchberger-M\"oller(BM) algorithm emerged, there has been wide interest in vanishing ideals of points and associated interpolation polynomials. Our paradigm is based on the theory of…
We study the complexity of polynomial multiplication over arbitrary fields. We present a unified approach that generalizes all known asymptotically fastest algorithms for this problem. In particular, the well-known algorithm for…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
On one hand, consider the problem of finding global solutions to a polynomial optimization problem and, on the other hand, consider the problem of interpolating a set of points with a complex exponential function. This paper proposes a…
Finding valid light paths that involve specular vertices in Monte Carlo rendering requires solving many non-linear, transcendental equations in high-dimensional space. Existing approaches heavily rely on Newton iterations in path space,…
We present a randomized algorithm for solving low-degree polynomial equation systems over finite fields faster than exhaustive search. In order to do so, we follow a line of work by Lokshtanov, Paturi, Tamaki, Williams, and Yu (SODA 2017),…
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…
In this article, the authors study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e.\,g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
A multivariate interpolation formula (MVIF) over finite fields is presented by using the proposed Kronecker delta function. The MVIF can be applied to yield polynomial relations over the base field among homogeneous symmetric rational…
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
In this paper, we first propose a general interpolation algorithm in a free module of a linearized polynomial ring, and then apply this algorithm to decode several important families of codes, Gabidulin codes, KK codes and MV codes. Our…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
We consider the problem of black-box function optimization over the boolean hypercube. Despite the vast literature on black-box function optimization over continuous domains, not much attention has been paid to learning models for…
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…