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Numerical Library Eigensolver Performance On Prace Tier-0 Systems

2017
*
Zenodo
*

Parallel eigensolver operations are at

doi:10.5281/zenodo.810719
fatcat:5d525xjwzbe2fnnhilcwal762q
*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. ...##
###
The Algorithm of Multiple Relatively Robust Representations for Multi-core Processors
[chapter]

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. ...

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

2021
*
arXiv
*
pre-print

We formulate

arXiv:2111.09750v2
fatcat:g2kbyld46vchtddhbbuaqgcqaq
*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. ...##
###
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]

1989
*
Solution of Superlarge Problems in Computational Mechanics
*

Dense Linear Algebra (DLA) is needed in

doi:10.1007/978-1-4613-0535-4_4
fatcat:bwi3sek6qfahfllclcxkgel5cu
*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*...##
###
A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations

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. ...

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

2000
*
Computational Methods in Science and Technology
*

Matrix approach extension

doi:10.12921/cmst.2000.06.01.73-100
fatcat:o5ikfyjlzzhulfh6raqqrggmie
*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 ...##
###
Abstract: A Novel Hybrid CPU-GPU Generalized Eigensolver for Electronic Structure Calculations Based on Fine Grained Memory Aware Tasks

2012
*
2012 SC Companion: High Performance Computing, Networking Storage and Analysis
*

Addressing these demands, we developed

doi:10.1109/sc.companion.2012.173
dblp:conf/sc/SolcaHTSD12
fatcat:jy4vxkbgjvhb3n33mqvvnwpy6a
*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 ...##
###
Progress in the numerical solution of the nonsymmetric eigenvalue problem

1995
*
Numerical Linear Algebra with Applications
*

KEY WORDS nonsymmetric matrices; sparse matrices; eigenvalue problem; EISPACK, M

doi:10.1002/nla.1680020304
fatcat:b3nhhhw6nzb55iypzjb5puhqlu
*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 ...##
###
JANPA: An open source cross-platform implementation of the Natural Population Analysis on the Java platform

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". ...

##
###
Divide and Conquer Symmetric Tridiagonal Eigensolver for Multicore Architectures

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. ...

##
###
An optimized and scalable eigensolver for sequences of eigenvalue problems

2014
*
Concurrency and Computation
*

Whenever is possible

doi:10.1002/cpe.3394
fatcat:jmfo25lagfg3hekyrsai2v4pwq
*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*. ...##
###
GPU-Acceleration of the ELPA2 Distributed Eigensolver for Dense Symmetric and Hermitian Eigenproblems
[article]

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*. ...

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

2014
*
arXiv
*
pre-print

Whenever it is possible

arXiv:1404.4161v2
fatcat:ccm4ylpsovbi3kp3s447gs53ou
*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. ...##
###
Framework for approximating eigenpairs in electronic structure computations

2004
*
Computing in science & engineering (Print)
*

CApE has several

doi:10.1109/mcse.2004.25
fatcat:sqxdurlatnew5jopz6wbmlisuu
*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*. ...
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