相关论文: A multistep strategy for polynomial system solving…

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…

Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…

We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \texttt{msolve} relies on Gr\''obner bases and…

A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…

We study the complexity of computing the real solutions of a bivariate polynomial system using the recently proposed algorithm BISOLVE. BISOLVE is a classical elimination method which first projects the solutions of a system onto the $x$-…

This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final…

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…

We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…

In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…

This paper describes a Buchberger-style algorithm to compute a Groebner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for…

This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order…

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…

Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…

Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…

Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…

Multivariate multipoint evaluation is the problem of evaluating a multivariate polynomial, given as a coefficient vector, simultaneously at multiple evaluation points. In this work, we show that there exists a deterministic algorithm for…

In this paper, we study the complexity of solving generic over-determined bilinear systems over a finite field $\mathbb{F}$. Given a generic bilinear sequence $B \in \mathbb{F}[\mathbf{x},\mathbf{y}]$, with respect to a partition of…