Related papers: A Triangular Decomposition Algorithm for Different…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented…
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…
A new concept, decomposition-unstable (DU) variety of a parametric polynomial system, is introduced in this paper and the stabilities of several triangular decomposition methods, such as characteristic set decomposition, relatively…
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
We develop the first fast spectral algorithm to decompose a random third-order tensor over $\mathbb{R}^d$ of rank up to $O(d^{3/2}/\text{polylog}(d))$. Our algorithm only involves simple linear algebra operations and can recover all…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…