Related papers: Multiplication in finite fields with Chudnovsky-ty…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…
Let $\mathbb F_{q^2}$ be the finite field with $q^2$ elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over $\mathbb F_{q^2}$ with many rational points. The curves…
In \cite{joux}, Joux devised an algorithm to compute discrete logarithms between elements in a certain subset of the multiplicative group of an extension of the finite field $\mathbb{F}_{p^n}$ in time polynomial in $p$ and $n$. Shortly…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method…
The restarted primal-dual hybrid gradient method (rPDHG) is a first-order method that has recently received significant attention for its computational effectiveness in solving linear program (LP) problems. Despite its impressive practical…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
We propose a new algorithm MARINLINGA for reverse line graph computation, i.e., constructing the original graph from a given line graph. Based on the completely new and simpler principle of link relabeling and endnode recognition,…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…
An adaptive procedure for constructing polynomials which are biorthogonal to the basis of monomials in the same finite-dimensional inner product space is proposed. By taking advantage of available orthogonal polynomials, the proposed…
Let $\Sigma \subset \mathbb{C}$ be a compact subset of the complex plane, and $\mu$ be a probability distribution on $\Sigma$. We give necessary and sufficient conditions for $\mu$ to be the weak* limit of a sequence of uniform probability…
New modifications of the methods for simultaneous extraction of all roots of polynomials over an arbitrary Chebyshev system are elaborated. A cubic convergence of iterations is proved. The method presented is a generalisation of the…
By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
Recently, Okounkov, Lazarsfeld and Mustata, and Kaveh and Khovanskii have shown that the growth of a graded linear series on a projective variety over an algebraically closed field is asymptotic to a polynomial. We give a complete…
In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be…
Graph propagation (GP) computation plays a crucial role in graph data analysis, supporting various applications such as graph node similarity queries, graph node ranking, graph clustering, and graph neural networks. Existing methods, mainly…