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Two global quasi-Newton algorithms for solving matrix polynomial equations
In this article, we globalize the quasi-Newton algorithm proposed in Macías et al. (Appl Math Comput 441:127678, 2023) introducing an exact line...
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Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization...
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Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms
In this work we extend some ideas about greedy algorithms, which are well-established tools for, e.g., kernel bases, and exponential-polynomial...
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Polynomial-time algorithms for multimarginal optimal transport problems with structure
Multimarginal Optimal Transport (MOT) has attracted significant interest due to applications in machine learning, statistics, and the sciences....
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A Survey on Computational Aspects of Polynomial Amoebas
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational...
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Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
The paper presents a novel method that allows one to establish numerical solutions of linear and nonlinear ordinary differential equations—with...
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Improved Complexity Analysis of Quasi-Polynomial Algorithms Solving Parity Games
We improve the complexity of solving parity games (with priorities in vertices) for...
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Fair allocation algorithms for indivisible items under structured conflict constraints
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict...
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New Results on Equivalence of Multivariate Polynomial Matrices
This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible...
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Implicitisation and Parameterisation in Polynomial Functors
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations....
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ReLU neural networks of polynomial size for exact maximum flow computation
This paper studies the expressive power of artificial neural networks with rectified linear units. In order to study them as a model of real-valued ...
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Polynomial-Time Approximability of the Asymmetric Problem of Covering a Graph by a Bounded Number of Cycles
Recently, O. Svensson and V. Traub have provided the first proof of the polynomial-time approximability of the asymmetric traveling salesman problem...
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Computational complexity and algorithms for two scheduling problems under linear constraints
This paper considers two different types of scheduling problems under linear constraints. The first is the single-machine scheduling problem with...
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Polynomial Factorization Over Henselian Fields
We present an algorithm that, given an irreducible polynomial g over a general valued field ( K , v ), finds the factorization of g over the...
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On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row...
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Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations
In this paper, the notion of rational univariate representations with variables is introduced. Consequently, the ideals, created by given rational...
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Numerical Differentiation by the Polynomial-Exponential Basis
AbstractOur objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can...
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Polynomial Total Positivity and High Relative Accuracy Through Schur Polynomials
In this paper, Schur polynomials are used to provide a bidiagonal decomposition of polynomial collocation matrices. The symmetry of Schur polynomials...
