A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems

Fengbo Ren, Chenxin Zhang, Liang Liu, Wenyao Xu, Viktor Owall, Dejan Marković

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

QR decomposition (QRD) is used to solve least-squares (LS) problems for a wide range of applications. However, traditional QR decomposition methods, such as Gram-Schmidt (GS), require high computational complexity and nonlinear operations to achieve high throughput, limiting their usage on resource-limited platforms. To enable efficient LS computation on embedded systems for real-time applications, this paper presents an alternative decomposition method, called QDRD, which relaxes system requirements while maintaining the same level of performance. Specifically, QDRD eliminates both the square-root operations in the normalization step and the divisions in the subsequent backward substitution. Simulation results show that the accuracy and reliability of factorization matrices can be significantly improved by QDRD, especially when executed on precision-limited platforms. Furthermore, benchmarking results on an embedded platform show that QDRD provides constantly better energy-efficiency and higher throughput than GS-QRD in solving LS problems. Up to 4 and 6.5 times improvement in energy-efficiency and throughput, respectively, can be achieved for small-size problems.

Original languageEnglish (US)
Article number6882128
Pages (from-to)73-76
Number of pages4
JournalIEEE Embedded Systems Letters
Volume6
Issue number4
DOIs
StatePublished - Dec 1 2014
Externally publishedYes

Fingerprint

Embedded systems
Decomposition
Throughput
Energy efficiency
Benchmarking
Factorization
Computational complexity
Substitution reactions

Keywords

  • Computational complexity
  • energy efficiency
  • least-squares problem
  • matrix factorization
  • QR decomposition

ASJC Scopus subject areas

  • Computer Science(all)
  • Control and Systems Engineering

Cite this

A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems. / Ren, Fengbo; Zhang, Chenxin; Liu, Liang; Xu, Wenyao; Owall, Viktor; Marković, Dejan.

In: IEEE Embedded Systems Letters, Vol. 6, No. 4, 6882128, 01.12.2014, p. 73-76.

Research output: Contribution to journalArticle

Ren, Fengbo ; Zhang, Chenxin ; Liu, Liang ; Xu, Wenyao ; Owall, Viktor ; Marković, Dejan. / A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems. In: IEEE Embedded Systems Letters. 2014 ; Vol. 6, No. 4. pp. 73-76.
@article{69f290d50b304095ac0ca54a74dcc43f,
title = "A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems",
abstract = "QR decomposition (QRD) is used to solve least-squares (LS) problems for a wide range of applications. However, traditional QR decomposition methods, such as Gram-Schmidt (GS), require high computational complexity and nonlinear operations to achieve high throughput, limiting their usage on resource-limited platforms. To enable efficient LS computation on embedded systems for real-time applications, this paper presents an alternative decomposition method, called QDRD, which relaxes system requirements while maintaining the same level of performance. Specifically, QDRD eliminates both the square-root operations in the normalization step and the divisions in the subsequent backward substitution. Simulation results show that the accuracy and reliability of factorization matrices can be significantly improved by QDRD, especially when executed on precision-limited platforms. Furthermore, benchmarking results on an embedded platform show that QDRD provides constantly better energy-efficiency and higher throughput than GS-QRD in solving LS problems. Up to 4 and 6.5 times improvement in energy-efficiency and throughput, respectively, can be achieved for small-size problems.",
keywords = "Computational complexity, energy efficiency, least-squares problem, matrix factorization, QR decomposition",
author = "Fengbo Ren and Chenxin Zhang and Liang Liu and Wenyao Xu and Viktor Owall and Dejan Marković",
year = "2014",
month = "12",
day = "1",
doi = "10.1109/LES.2014.2350997",
language = "English (US)",
volume = "6",
pages = "73--76",
journal = "IEEE Embedded Systems Letters",
issn = "1943-0663",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",

}

TY - JOUR

T1 - A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems

AU - Ren, Fengbo

AU - Zhang, Chenxin

AU - Liu, Liang

AU - Xu, Wenyao

AU - Owall, Viktor

AU - Marković, Dejan

PY - 2014/12/1

Y1 - 2014/12/1

N2 - QR decomposition (QRD) is used to solve least-squares (LS) problems for a wide range of applications. However, traditional QR decomposition methods, such as Gram-Schmidt (GS), require high computational complexity and nonlinear operations to achieve high throughput, limiting their usage on resource-limited platforms. To enable efficient LS computation on embedded systems for real-time applications, this paper presents an alternative decomposition method, called QDRD, which relaxes system requirements while maintaining the same level of performance. Specifically, QDRD eliminates both the square-root operations in the normalization step and the divisions in the subsequent backward substitution. Simulation results show that the accuracy and reliability of factorization matrices can be significantly improved by QDRD, especially when executed on precision-limited platforms. Furthermore, benchmarking results on an embedded platform show that QDRD provides constantly better energy-efficiency and higher throughput than GS-QRD in solving LS problems. Up to 4 and 6.5 times improvement in energy-efficiency and throughput, respectively, can be achieved for small-size problems.

AB - QR decomposition (QRD) is used to solve least-squares (LS) problems for a wide range of applications. However, traditional QR decomposition methods, such as Gram-Schmidt (GS), require high computational complexity and nonlinear operations to achieve high throughput, limiting their usage on resource-limited platforms. To enable efficient LS computation on embedded systems for real-time applications, this paper presents an alternative decomposition method, called QDRD, which relaxes system requirements while maintaining the same level of performance. Specifically, QDRD eliminates both the square-root operations in the normalization step and the divisions in the subsequent backward substitution. Simulation results show that the accuracy and reliability of factorization matrices can be significantly improved by QDRD, especially when executed on precision-limited platforms. Furthermore, benchmarking results on an embedded platform show that QDRD provides constantly better energy-efficiency and higher throughput than GS-QRD in solving LS problems. Up to 4 and 6.5 times improvement in energy-efficiency and throughput, respectively, can be achieved for small-size problems.

KW - Computational complexity

KW - energy efficiency

KW - least-squares problem

KW - matrix factorization

KW - QR decomposition

UR - http://www.scopus.com/inward/record.url?scp=84913532509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84913532509&partnerID=8YFLogxK

U2 - 10.1109/LES.2014.2350997

DO - 10.1109/LES.2014.2350997

M3 - Article

AN - SCOPUS:84913532509

VL - 6

SP - 73

EP - 76

JO - IEEE Embedded Systems Letters

JF - IEEE Embedded Systems Letters

SN - 1943-0663

IS - 4

M1 - 6882128

ER -