English
Related papers

Related papers: Accelerating the Computation of Tensor $Z$-eigenva…

200 papers

Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is…

Numerical Analysis · Mathematics 2022-05-02 Daan Camps , Thomas Mach , Raf Vandebril , David S. Watkins

Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…

Data Structures and Algorithms · Computer Science 2024-06-07 Vivek Bharadwaj , Beheshteh T. Rakhshan , Osman Asif Malik , Guillaume Rabusseau

In the recent years, multi-core processor designs have found their way into many computing devices. To exploit the capabilities of such devices in the best possible way, signal processing algorithms have to be adapted to an operation in…

Image and Video Processing · Electrical Eng. & Systems 2022-07-04 Jürgen Seiler , André Kaup

Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow…

Optimization and Control · Mathematics 2023-06-13 Haoya Li , Hsiang-fu Yu , Lexing Ying , Inderjit Dhillon

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

Artificial Intelligence · Computer Science 2022-05-05 Zarathustra A. Goertzel , Jan Jakubův , Cezary Kaliszyk , Miroslav Olšák , Jelle Piepenbrock , Josef Urban

For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear…

Optimization and Control · Mathematics 2021-10-05 M. Marques Alves

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…

Numerical Analysis · Mathematics 2022-09-13 Utkarsh , Chris Elrod , Yingbo Ma , Christopher Rackauckas

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…

Numerical Analysis · Mathematics 2025-02-07 Ratikanta Behera , Saroja Kumar Panda , Jajati Keshari Sahoo

This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to…

Numerical Analysis · Mathematics 2021-05-12 Andersen Man Shun Ang , Jeremy E. Cohen , Nicolas Gillis , Le Thi Khanh Hien

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…

Numerical Analysis · Computer Science 2020-11-10 Krzysztof Domino , Piotr Gawron , Łukasz Pawela

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…

Optimization and Control · Mathematics 2018-06-21 Robert M. Gower , Filip Hanzely , Peter Richtárik , Sebastian Stich

We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…

Methodology · Statistics 2018-10-30 Mahito Sugiyama , Hiroyuki Nakahara , Koji Tsuda

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…

Information Theory · Computer Science 2016-11-17 Karsten Fyhn , Marco F. Duarte , Søren Holdt Jensen

We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-04 Daniel Bourgeois , Zhimin Ding , Dimitrije Jankov , Jiehui Li , Mahmoud Sleem , Yuxin Tang , Jiawen Yao , Xinyu Yao , Chris Jermaine

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…

Numerical Analysis · Computer Science 2015-08-24 Alex Pereira da Silva , Pierre Comon , Andre Lima Ferrer de Almeida

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Numerical Analysis · Mathematics 2025-10-21 Nicolas A. Barnafi , Felipe Galarce , Pablo Brubeck

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…

Statistical Mechanics · Physics 2023-04-17 Li-Ping Yang , Y. F. Fu , Z. Y. Xie , T. Xiang

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

Numerical Analysis · Mathematics 2013-12-31 Na Li , Carmeliza Navasca

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…

Optimization and Control · Mathematics 2021-01-14 Dmitry Pasechnyuk , Anton Anikin , Vladislav Matyukhin

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…

Computational Physics · Physics 2024-05-01 Adela Habib , Joshua Finkelstein , Anders M. N. Niklasson