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Hardware architectures for eigenvalue computation of real symmetric matrices

Y. Liu, C.-S. Bouganis, P.Y.K. Cheung
2009 IET Computers & Digital Techniques  
The problem of eigenvalue computation of real symmetric matrices is focused upon.  ...  When the application of interest requires the computation of eigenvalues of high throughput or realtime performance, a hardware implementation of an eigenvalue computation block is often employed.  ...  Introduction The computation of eigenvalues for symmetric matrices is essential in many applications.  ... 
doi:10.1049/iet-cdt:20080008 fatcat:inxhozs2yreyjjiguifbjc7p44

Hardware Efficient Architectures for Eigenvalue Computation

Yang Liu, C.-S. Bouganis, P.Y.K. Cheung, P.H.W. Leong, S.J. Motley
2006 Proceedings of the Design Automation & Test in Europe Conference  
This paper focuses on the exploration of hardware architectures which compute eigenvalues of symmetric matrices.  ...  Eigenvalue computation is essential in many fields of science and engineering. For high performance and real-time applications, this may need to be done in hardware.  ...  Pipelined architectures for 3 × 3 symmetric matrices In very high speed applications, such as real time optical flow computation [1] , massive throughput of the smallest eigenvalues of 3 × 3 matrices  ... 
doi:10.1109/date.2006.243838 dblp:conf/date/LiuBCLM06 fatcat:rk7v3ks2c5hxbbviicmj7k6sxa

High Level Synthesis FPGA Implementation of the Jacobi Algorithm to Solve the Eigen Problem

Ignacio Bravo, César Vázquez, Alfredo Gardel, José L. Lázaro, Esther Palomar
2015 Mathematical Problems in Engineering  
The computation of eigenvalues and eigenvectors has many applications where real time processing is required, and thus hardware implementations are often mandatory.  ...  We present a hardware implementation of the Jacobi algorithm to compute the eigenvalue decomposition (EVD).  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/870569 fatcat:adgqcw6x7vb5jl76a4jvylny2i

Numerical Library Eigensolver Performance On Prace Tier-0 Systems

Andrew Sunderland
2017 Zenodo  
This project analyses parallel performance of established and newly developed parallel dense symmetric eigensolver numerical library routines on PRACE Tier-0 systems using real datasets from large-scale  ...  Parallel eigensolver operations are at the computational core of many large-scale scientific and engineering 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

Computation of exact inertia and inclusions of eigenvalues (singular values) of tridiagonal (bidiagonal) matrices

K.V. Fernando
2007 Linear Algebra and its Applications  
Similarly, using the Golub-Kahan form, guaranteed intervals for singular values of bidiagonal matrices can be computed.  ...  In this paper, we describe an algorithm in floating-point arithmetic to compute the exact inertia of a real symmetric (shifted) tridiagonal matrix.  ...  Author wishes to thank Timothy Fernando for computational  ... 
doi:10.1016/j.laa.2006.09.008 fatcat:axymf3fbdjhe5h7dqnojwuphce

An Efficient Architecture for Floating-Point Eigenvalue Decomposition

Xinying Wang, Joseph Zambreno
2014 2014 IEEE 22nd Annual International Symposium on Field-Programmable Custom Computing Machines  
EVD is considered computationally expensive, and as software implementations have not been able to meet the performance requirements of many real-time applications, the use of reconfigurable computing  ...  In this paper, we present an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices.  ...  In this paper, we present a novel and efficient FPGAbased architecture for eigenvalue decomposition, which attempts to analyze considerably larger matrices than those applied to previous hardware designs  ... 
doi:10.1109/fccm.2014.27 dblp:conf/fccm/WangZ14 fatcat:yco3yk34fvat5pwrmoiezebgba

An Efficient GPU Implementation of Bulk Computation of the Eigenvalue Problem for Many Small Real Non-symmetric Matrices

Hiroki Tokura, Takumi Honda, Yasuaki Ito, Koji Nakano, Mitsuya Nishino, Yushiro Hirota, Masami Saeki
2017 International Journal of Networking and Computing  
The main contribution of this paper is to present an efficient GPU implementation of bulk computation of eigenvalues for many small, non-symmetric, real matrices.  ...  This work is motivated by the necessity of such bulk computation in designing of control systems, which requires to compute the eigenvalues of hundreds of thousands non-symmetric real matrices of size  ...  Especially, we focus on the eigenvalues computation for a square, non-symmetric real matrix. There are several algorithms of computing eigenvalues for non-symmetric matrices.  ... 
doi:10.15803/ijnc.7.2_227 fatcat:zfrcxqdzdvf7dbd664oa3kt4pu

A High Throughput FPGA-Based Implementation of the Lanczos Method for the Symmetric Extremal Eigenvalue Problem [chapter]

Abid Rafique, Nachiket Kapre, George A. Constantinides
2012 Lecture Notes in Computer Science  
This paper presents a streaming architecture comprising floating-point operators coupled with highbandwidth on-chip memories for the Lanczos method, an iterative algorithm for symmetric eigenvalues computation  ...  We show the Lanczos method can be specialized only for extremal eigenvalues computation and present an architecture which can achieve a sustained single precision floating-point performance of 175 GFLOPs  ...  Bisection Method The bisection method is an efficient method for finding the eigenvalues of a symmetric tridiagonal matrix T k and it has a computational complexity of Θ(k) for extremal eigenvalue computation  ... 
doi:10.1007/978-3-642-28365-9_20 fatcat:lrzajxujfna5bmxgk4ayq7zfty

Real-Time Digital Signal Processing Based on FPGAs for Electronic Skin Implementation †

Ali Ibrahim, Paolo Gastaldo, Hussein Chible, Maurizio Valle
2017 Sensors  
Results demonstrate the feasibility of the proposed implementation when real-time classification of input touch modalities are targeted.  ...  In this framework, this paper presents the implementation of digital signal processing based on FPGAs for tactile data processing.  ...  Acknowledgments: This work is supported by the University of Genova-Progetti di Ricerca di Ateneo 2014: Electronic skin for prosthetic systems, resp. M. Valle.  ... 
doi:10.3390/s17030558 pmid:28287448 pmcid:PMC5375844 fatcat:hwgffzuakbb3tklbmyifgcrbzi

MRRR-based Eigensolvers for Multi-core Processors and Supercomputers [article]

Matthias Petschow
2014 arXiv   pre-print
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems  ...  To compute k eigenpairs of a real n-by-n tridiagonal T, MRRR only requires O(kn) arithmetic operations; in contrast, all the other practical methods require O(k^2 n) or O(n^3) operations in the worst case  ...  The above tests were limited to computing all eigenpairs of real symmetric matrices.  ... 
arXiv:1401.4950v1 fatcat:iiillrtypva3tmpv2d5mlmrkai

Solving Large Top-K Graph Eigenproblems with a Memory and Compute-optimized FPGA Design [article]

Francesco Sgherzi, Alberto Parravicini, Marco Siracusa, Marco Domenico Santambrogio
2021 arXiv   pre-print
Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods.  ...  In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and unnecessary, as spectral methods can retrieve the relevant properties of enormous graphs using just  ...  The Jacobi Eigenvalue Algorithm The Jacobi eigenvalue algorithm computes the eigenvalues and eigenvectors of a dense symmetric real matrix.  ... 
arXiv:2103.10040v1 fatcat:x6yo6juk4zaffabnsf5cl3wnaa

MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures

M. Petschow, P. Bientinesi
2011 Parallel Computing  
The computation of eigenvalues and eigenvectors of symmetric tridiagonal matrices arises frequently in applications; often as one of the steps in the solution of Hermitian and symmetric eigenproblems.  ...  We show that in most cases MR 3 -SMP is faster and achieves better speedups than state-of-the-art eigensolvers for uni-processors and distributedmemory systems.  ...  Acknowledgment The authors wish to thank the Center for Computing and Communication at RWTH Aachen for the resources, Diego Fabregat and Roman Iakymchuk for suggestions on an earlier draft of the paper  ... 
doi:10.1016/j.parco.2011.10.001 fatcat:ewevz5uxhrcytepjizikl36vja

Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method

A. Dziekonski, M. Mrozowski
2018 Radioengineering  
This paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higher-order finite element method  ...  The performance of the solver is tested for single and dual GPU hardware setups, making use of two types of GPU: NVIDIA Kepler K40s and NVIDIA Pascal P100s.  ...  The Pascal P100 GPU was purchased using statutory funds provided by the Faculty of Electronics, Telecommunications, and Informatics at Gdańsk University of Technology.  ... 
doi:10.13164/re.2018.0930 fatcat:oxssj7clwra73homyuqt5u7l44

An Efficient VLSI Architecture for FastICA by using the Algebraic Jacobi Method for EVD

Muhammad Sajjad, Mohd Zuki Yusoff, Norashikin Yahya, Ali Shahbaz Haider
2021 IEEE Access  
Data whitening mainly consists of eigenvalue decomposition (EVD), whereas WVE consists of matrices multiplications and non-linearity computation.  ...  In [12] , a hardware architecture for a cost-effective 16-channels FastICA is reported for the processing of electroencephalographic (EEG) signals in real-time.  ...  MUHAMMAD SAJJAD Currently, she holds a position of senior lecturer in UTP and also a member of Centre for Intelligent Signal and Imaging Research (CISIR), one of the Malaysia National Higher Institution  ... 
doi:10.1109/access.2021.3072495 fatcat:h6pinpsqf5gxbce6q5g5626rue

A direct method for completing eigenproblem solutions on a parallel computer

Roy O. Davies, J.J. Modi
1986 Linear Algebra and its Applications  
The computation of eigenvalues and eigenvectors of a real symmetric matrix A with distinct eigenvalues can be speeded up at the end of the Jacobi process when the off-diagonal elements have become sufficiently  ...  small for A to be regarded as a perturbation of a diagonal matrix.  ...  Pryce for his valuable comments, and two referees for helpful suggestions.  ... 
doi:10.1016/0024-3795(86)90162-x fatcat:fcoyufte6naonkh77nmklu4p3m
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