Related papers: Tensor computations in computer algebra systems
Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad-hoc…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree of the input equations and exponential in their…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
We show how the numerical range of a matrix can be used to bound the optimal value of certain optimization problems over real tensor product vectors. Our bound is stronger than the trivial bounds based on eigenvalues, and can be computed…
In this paper we explore the possibility of using computational algebraic methods to analyze a class of consensus protocols. We state some necessary conditions for convergence under consensus protocols that are polynomials.
Tensor cores are specialized processing units within GPUs that have demonstrated significant efficiency gains in compute-bound applications such as Deep Learning Training by accelerating dense matrix operations. Given their success,…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to…