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Numerical Library Eigensolver Performance On Prace Tier-0 Systems

Andrew Sunderland
2017 Zenodo  
Parallel eigensolver operations are at the computational core of many large-scale scientific and engineering application codes.  ...  application codes.  ...  The author would also like to express his gratitude to Ian Bush of NAG Ltd and Hermann Lederer of RZG in Germany.  ... 
doi:10.5281/zenodo.810719 fatcat:5d525xjwzbe2fnnhilcwal762q

The Algorithm of Multiple Relatively Robust Representations for Multi-core Processors [chapter]

Matthias Petschow, Paolo Bientinesi
2012 Lecture Notes in Computer Science  
The algorithm of Multiple Relatively Robust Representations (MRRR or MR 3 ) computes k eigenvalues and eigenvectors of a symmetric tridiagonal matrix in O(nk) arithmetic operations.  ...  In this paper we discuss some of the issues and trade-offs arising in the design of MR 3 -SMP, an algorithm for multi-core CPUs and SMP systems.  ...  Acknowledgment The authors wish to thank the Center for Computing and Communication RWTH Aachen for the resources to run all the experiments, Diego Fabregat and Roman Iakymchuck for discussions.  ... 
doi:10.1007/978-3-642-28151-8_15 fatcat:zjfp5n2wvfawffvfamazz7mxcy

The self-consistent field iteration for p-spectral clustering [article]

Parikshit Upadhyaya, Elias Jarlebring, Francesco Tudisco
2021 arXiv   pre-print
We formulate the p-Laplacian eigenproblem as a type of nonlinear eigenproblem with one eigenvector nonlinearity , which then allows us to adapt the SCF iteration for its solution after the application  ...  The self-consistent field (SCF) iteration, combined with its variants, is one of the most widely used algorithms in quantum chemistry.  ...  The work of the second author was partially carried out during a research visit supported by EPFL/Univ. Geneva.  ... 
arXiv:2111.09750v2 fatcat:g2kbyld46vchtddhbbuaqgcqaq

Page 2700 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Several results taken from quantum chemistry, acoustics, and structural mechanics are presented that show the superiority of MINRES and the new MINERR method over SYMMLQ, especially for ill-conditioned  ...  (ii) Find the spectrum of a given symmetric-definite matrix pen- cil. (iii) Solve the additive inverse eigenvalue problem for a given symmetric-definite pencil. Alan L.  ... 

A Project for Developing a Linear Algebra Library for High-Performance Computers [chapter]

J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, D. Sorensen
1989 Solution of Superlarge Problems in Computational Mechanics  
Dense Linear Algebra (DLA) is needed in a wide variety of science and engineering applications: • Linear systems: Solve Ax = b • Computational electromagnetics, material science, applications using boundary  ...  • Traditional libraries like MAGMA can be used as backend to accelerate the LA computations in data analytics applications • Need support for 1) New data layouts, 2) Acceleration for small matrix computations  ...  the computation for every pixel value O n,k is a tensor contraction: • Plenty of parallelism; small operations that must be batched • With data "reshape" the computation can be transformed into a  ... 
doi:10.1007/978-1-4613-0535-4_4 fatcat:bwi3sek6qfahfllclcxkgel5cu

A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations

Paolo Bientinesi, Inderjit S. Dhillon, Robert A. van de Geijn
2005 SIAM Journal on Scientific Computing  
Algorithm MR 3 has a complexity of O(n 2 ) operations for computing all eigenvalues and eigenvectors of a symmetric tridiagonal problem.  ...  We present comparisons with other eigensolvers and results on matrices that arise in the applications of computational quantum chemistry and finite element modeling of automobile bodies.  ...  We are indebted to the Center for Computational Research at the University at Buffalo, SUNY, for the use of their 300 compute node Dell Linux Cluster.  ... 
doi:10.1137/030601107 fatcat:w56ohdtiang3dow5ham2cshm6u

NUMERICAL MATRIX METHOD FOR SOLVING STATIONARY ONE-DIMENSIONAL SCHRÖDINGER EQUATION. AMSSE PROGRAM

WŁODZIMIERZ SALEJDA, MARCIN JUST, MICHAŁ H. TYC
2000 Computational Methods in Science and Technology  
Matrix approach extension to the case of an effective-mass equation is mentioned.  ...  In the framework of the proposed approach, SODSE is converted into an algebraic eigenvalue problem, which represents a discrete version of studied problem on an equally spaced grid.  ...  I Example results from the PTEST 1 application for the harmonic oscillator potential (8) with a quasi-symmetric tridiagonal matrix [19] A (q-s) the obtained eigenproblem(8)is  ... 
doi:10.12921/cmst.2000.06.01.73-100 fatcat:o5ikfyjlzzhulfh6raqqrggmie

Abstract: A Novel Hybrid CPU-GPU Generalized Eigensolver for Electronic Structure Calculations Based on Fine Grained Memory Aware Tasks

Raffaele Solca, Azzam Haidar, Stanimire Tomov, Thomas C. Schulthess, Jack Dongarra
2012 2012 SC Companion: High Performance Computing, Networking Storage and Analysis  
Addressing these demands, we developed a generalized eigensolver featuring novel algorithms of increased computational intensity (compared with the standard algorithms), decomposition of the computation  ...  However, hybrid systems call for the development of new algorithms that efficiently exploit heterogeneity and massive parallelism of not just GPUs, but of multicore/manycore CPUs as well.  ...  This has opened many new acceleration opportunities in electronic structure calculations for materials science and chemistry applications, where the problems are too small to effectively scale on distributed  ... 
doi:10.1109/sc.companion.2012.173 dblp:conf/sc/SolcaHTSD12 fatcat:jy4vxkbgjvhb3n33mqvvnwpy6a

Progress in the numerical solution of the nonsymmetric eigenvalue problem

Zhaojun Bai
1995 Numerical Linear Algebra with Applications  
KEY WORDS nonsymmetric matrices; sparse matrices; eigenvalue problem; EISPACK, M A C K [44] is an elegant source for studying the state of the art in large eigenproblem techniques.  ...  In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.  ...  In particular, the author is grateful for the unique opportunity of visiting IMA at University of Minnesota during its [1991][1992] Applied Linear Algebra year, and being able to communicate on this subject  ... 
doi:10.1002/nla.1680020304 fatcat:b3nhhhw6nzb55iypzjb5puhqlu

JANPA: An open source cross-platform implementation of the Natural Population Analysis on the Java platform

Tymofii Y. Nikolaienko, Leonid A. Bulavin, Dmytro M. Hovorun
2014 Computational and Theoretical Chemistry  
The package consists of three programs: two of them generate MOLDEN files from the output of popular quantum chemistry packages (PSI4, ORCA, NwChem, Gaussian, GAMESS-US etc.), and one program performs  ...  The algorithms for constructing natural atomic orbitals (NAOs) from a reduced one-particle density matrix as well as for natural population analysis (NPA) are reviewed and their novel independent crossplatform  ...  Acknowledgments The authors are grateful for computational resources provided by High-Performance Computing Center of National Technical University of Ukraine "Kyiv Polytechnic Institute".  ... 
doi:10.1016/j.comptc.2014.10.002 fatcat:2pq4xvunrnakraz2a66vk3zep4

Divide and Conquer Symmetric Tridiagonal Eigensolver for Multicore Architectures

Gregoire Pichon, Azzam Haidar, Mathieu Faverge, Jakub Kurzak
2015 2015 IEEE International Parallel and Distributed Processing Symposium  
Computing eigenpairs of a symmetric matrix is a problem arising in many industrial applications, including quantum physics and finite-elements computation for automobiles.  ...  In this article, we focus on solving the tridiagonal eigenproblem, and we describe a novel implementation of the Divide and Conquer algorithm.  ...  The symmetric eigenproblem is a problem arising in many applications, such as quantum physics, chemistry and statistics.  ... 
doi:10.1109/ipdps.2015.51 dblp:conf/ipps/PichonHFK15 fatcat:uivnejaibbgabg6xagg77rf27m

An optimized and scalable eigensolver for sequences of eigenvalue problems

Mario Berljafa, Daniel Wortmann, Edoardo Di Napoli
2014 Concurrency and Computation  
Whenever is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be a correlated.  ...  In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems.  ...  We show a typical example of eigenproblem sequences as they arise in material science and quantum chemistry by presenting their emergence from one of the methods used in DFT computations.  ... 
doi:10.1002/cpe.3394 fatcat:jmfo25lagfg3hekyrsai2v4pwq

GPU-Acceleration of the ELPA2 Distributed Eigensolver for Dense Symmetric and Hermitian Eigenproblems [article]

Victor Wen-zhe Yu, Jonathan Moussa, Pavel Kůs, Andreas Marek, Peter Messmer, Mina Yoon, Hermann Lederer, Volker Blum
2021 arXiv   pre-print
The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed  ...  Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers.  ...  The ubiquitous adoption of graphics processing units (GPU) in highperformance computing opens up new opportunities to accelerate the solution of dense eigenproblems.  ... 
arXiv:2002.10991v4 fatcat:khp5rdi7lvhfzn2nesknyo7gju

An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems [article]

Mario Berljafa AICES, RWTH Aachen)
2014 arXiv   pre-print
Whenever it is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be correlated.  ...  In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems.  ...  A considerable subset of applications requires the solution of not just one eigenproblem but a sequence of them.  ... 
arXiv:1404.4161v2 fatcat:ccm4ylpsovbi3kp3s447gs53ou

Framework for approximating eigenpairs in electronic structure computations

W.N. Gansterer, Yihua Bai, R.M. Day, R.C. Ward
2004 Computing in science & engineering (Print)  
CApE has several algorithmic tools that both detect matrix structure in application problems and compute solutions to prescribed accuracy.  ...  Our framework, Computing Approximate Eigensystems (CApE), efficiently approximates symmetric linear eigenvalue problems occurring in the self-consistent field method used during electronic structure computations  ...  We are also investigating and analyzing a new approach for the eigenvector computation in the BD&C algorithm.  ... 
doi:10.1109/mcse.2004.25 fatcat:sqxdurlatnew5jopz6wbmlisuu
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