Related papers: A Basis-preserving Algorithm for Computing the Bez…

We show a method for constructing a polynomial interpolating roots' multiplicities of another polynomial, that does not use companion matrices. This leads to a modification to Guersenzvaig--Szechtman square-free decomposition algorithm that…

A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The technique is motivated by the effectiveness of local nonlinear smoothers at overcoming strong…

This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…

We consider computational and implementation issues for the completion of monomial sets to involution using different involutive divisions. Every of these divisions produces its own completion procedure. For the polynomial case it yields an…

In [5] Cauchon introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras…

Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is called a connection matrix.These matrices, a generalization…

Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…

We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and…

The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…

I recently proposed a method of bosonization valid for systems of an even number of fermions whose partition function is dominated at low energy by bosonic composites. This method respects all symmetries, in particular fermion number…

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass…

While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…

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 consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of…

In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a…

We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.

This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is…