Related papers: New bounds and efficient algorithm for sparse diff…
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
Robust mean estimation is one of the most important problems in statistics: given a set of samples in $\mathbb{R}^d$ where an $\alpha$ fraction are drawn from some distribution $D$ and the rest are adversarially corrupted, we aim to…
We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying…
We suggest an efficient algorithm for the selection of sparse subsets of a set of influence for the numerical discretization of differential operators on irregular nodes with polynomial consistency of a given order with the help of the QR…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of…
Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
The resultant of two univariate polynomials is an invariant of great importance in commutative algebra and vastly used in computer algebra systems. Here we present an algorithm to compute it over Artinian principal rings with a modified…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
In this paper we present two algorithms for the multiplication of sparse Laurent polynomials and Poisson series (the latter being algebraic structures commonly arising in Celestial Mechanics from the application of perturbation theories).…
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…
In this paper, we present a probabilistic algorithm to multiply two sparse polynomials almost as efficiently as two dense univariate polynomials with a result of approximately the same size. The algorithm depends on unproven heuristics that…