Fast givens rotation approach to second order sequential best rotation algorithms

Faizan Ahmad Khattak; Stephan Weiss; Ian Proudler

Fast givens rotation approach to second order sequential best rotation algorithms

Faizan Ahmad Khattak, Stephan Weiss, Ian Proudler

Electronic And Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

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Abstract

The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximated polynomial eigenvalues and eigen-vectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2's proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.

Original language	English
Number of pages	5
Publication status	Published - 15 Sept 2021
Event	International Conference in Sensor Signal Processing for Defence: from Sensor to Decision - Edinburgh, United Kingdom Duration: 14 Sept 2021 → 15 Sept 2021 Conference number: 10 https://sspd.eng.ed.ac.uk

Conference

Conference	International Conference in Sensor Signal Processing for Defence
Abbreviated title	SSPD
Country/Territory	United Kingdom
City	Edinburgh
Period	14/09/21 → 15/09/21
Internet address	https://sspd.eng.ed.ac.uk

Keywords

sequential best rotation (SBR2)
Givens rotation
algorithm
polynomial eigenvalues
broadband signals

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Khattak-etal-SSPD-2021-Fast-givens-rotation-approach-to-second-orderAccepted author manuscript, 650 KB

Cite this

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title = "Fast givens rotation approach to second order sequential best rotation algorithms",

abstract = "The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximated polynomial eigenvalues and eigen-vectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2's proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.",

keywords = "sequential best rotation (SBR2), Givens rotation, algorithm, polynomial eigenvalues, broadband signals",

author = "Khattak, {Faizan Ahmad} and Stephan Weiss and Ian Proudler",

year = "2021",

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day = "15",

language = "English",

note = "International Conference in Sensor Signal Processing for Defence : from Sensor to Decision, SSPD ; Conference date: 14-09-2021 Through 15-09-2021",

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TY - CONF

T1 - Fast givens rotation approach to second order sequential best rotation algorithms

AU - Khattak, Faizan Ahmad

AU - Weiss, Stephan

AU - Proudler, Ian

N1 - Conference code: 10

PY - 2021/9/15

Y1 - 2021/9/15

N2 - The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximated polynomial eigenvalues and eigen-vectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2's proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.

AB - The second order sequential best rotation (SBR2) algorithm is a popular algorithm to decompose a parahermitian matrix into approximated polynomial eigenvalues and eigen-vectors. The work horse behind SBR2 is a Givens rotation interspersed by delay operations. In this paper, we investigate and analyse the application of a fast Givens rotation in order to reduce the computation complexity of SBR2. The proposed algorithm inherits the SBR2's proven convergence to a diagonalised and spectrally majorised solution for the polynomial eigenvalues. We provide some analysis and examples for the execution speed of this fast Givens-based SBR2 compared to a standard SBR2 implementation.

KW - sequential best rotation (SBR2)

KW - Givens rotation

KW - algorithm

KW - polynomial eigenvalues

KW - broadband signals

UR - https://sspd.eng.ed.ac.uk/

M3 - Paper

T2 - International Conference in Sensor Signal Processing for Defence

Y2 - 14 September 2021 through 15 September 2021

ER -

Fast givens rotation approach to second order sequential best rotation algorithms

Abstract

Conference

Keywords

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Signal Processing in the Information Age (UDRC III)

Cite this

Fast givens rotation approach to second order sequential best rotation algorithms

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Cite this