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Related papers: Novel Modifications of Parallel Jacobi Algorithms

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Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Numerical Analysis · Mathematics 2019-02-08 Per-Gunnar Martinsson

We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…

Optimization and Control · Mathematics 2024-06-12 Arun Jambulapati , Aaron Sidford , Kevin Tian

Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-19 Edgar Solomonik , Grey Ballard , James Demmel , Torsten Hoefler

We present a new software, HYPPO, that enables the automatic tuning of hyperparameters of various deep learning (DL) models. Unlike other hyperparameter optimization (HPO) methods, HYPPO uses adaptive surrogate models and directly accounts…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-24 Ioannis Sakiotis , Kamesh Arumugam , Marc Paterno , Desh Ranjan , Balša Terzić , Mohammad Zubair

We present a new $O(k^2 \binom{n}{k}^2)$ method for generating an orthogonal basis of eigenvectors for the Johnson graph $J(n,k)$. Unlike standard methods for computing a full eigenbasis of sparse symmetric matrices, the algorithm presented…

Data Structures and Algorithms · Computer Science 2018-12-12 Jackson Abascal , Amadou Bah , Mario Banuelos , David Uminsky , Olivia Vasquez

Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue…

Computational Physics · Physics 2017-09-13 Yan Pan , Xiaoying Dai , Stefano de Gironcoli , Xin-Gao Gong , Gian-Marco Rignanese , Aihui Zhou

In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…

Optimization and Control · Mathematics 2008-09-23 Dang Doan , Tamas Keviczky , Ion Necoara , Moritz Diehl

We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…

Machine Learning · Computer Science 2023-02-08 Yash Chandak , Shiv Shankar , Venkata Gandikota , Philip S. Thomas , Arya Mazumdar

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Computer Vision and Pattern Recognition · Computer Science 2022-03-23 Aleksandr Ermolov , Leyla Mirvakhabova , Valentin Khrulkov , Nicu Sebe , Ivan Oseledets

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in…

Quantum Physics · Physics 2016-06-28 Mona Arabzadeh , Mahboobeh Houshmand , Mehdi Sedighi , Morteza Saheb Zamani

Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…

Numerical Analysis · Mathematics 2021-10-19 Michiel E. Hochstenbach , Bor Plestenjak

We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi…

Classical Analysis and ODEs · Mathematics 2020-12-15 Antonio J. Durán , Manuel D. de la Iglesia

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…

Quantum Physics · Physics 2009-01-23 Daniel S. Abrams , Seth Lloyd

In this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums…

Number Theory · Mathematics 2024-01-19 Ce Xu , Jianqiang Zhao

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…

Numerical Analysis · Mathematics 2013-10-08 Emre Mengi

This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which can be solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control…

Optimization and Control · Mathematics 2024-12-18 Simo Särkkä , Ángel F. García-Fernández

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and…

Machine Learning · Computer Science 2021-06-15 Yang Song , Chenlin Meng , Renjie Liao , Stefano Ermon

The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-12-14 Nadezhda A. Ezhova , Leonid B. Sokolinsky