Matrix operations for the simulation and immediate reverse-engineering of time series data

Michael A. Idowu, James L. Bown

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)
21 Downloads (Pure)

Abstract

We present a new method for constructing and decomposing square matrices. This method, based on the computed parameterisation of their implied determinants and minors, operates on the product of factors of a new form of matrix decomposition. This method may be employed to build new matrices with fixed determinant(s). We demonstrate that this new approach is fundamentally well-connected to the Cholesky decomposition if applied on symmetric matrices. We also demonstrate that it is related to the LU decomposition method via a diagonal matrix multiplier. Also through this new method a direct relation between Cholesky decomposition and LU factorisation is shown. This method, presented for the first time, is useful for (re)constructing matrices with a predefined determinant and simulating inverse problems. The inference method introduced here also is based on new matrix manipulation techniques that we have developed for the identification of systems from reproducible time series data.
Original languageEnglish
Title of host publicationProceedings
Subtitle of host publication2012 14th International Conference on Modelling and Simulation
EditorsDavid Al-Dabass, Alessandra Orsoni, Richard Cant
Place of PublicationPiscataway, NJ
PublisherIEEE
Pages101-106
Number of pages6
ISBN (Electronic)9780769546827
ISBN (Print)9781467313667
DOIs
Publication statusPublished - 2012
Event14th International Conference on Computer Modelling and Simulation - Cambridge, United Kingdom
Duration: 28 Mar 201230 Mar 2012
Conference number: 14

Conference

Conference14th International Conference on Computer Modelling and Simulation
Abbreviated titleUKSim 2012
CountryUnited Kingdom
CityCambridge
Period28/03/1230/03/12

Fingerprint

Reverse Engineering
Time Series Data
Cholesky Decomposition
Determinant
Simulation
LU decomposition
LU Factorization
Matrix Decomposition
Diagonal matrix
Square matrix
Decomposition Method
Symmetric matrix
Parameterization
Demonstrate
Multiplier
Manipulation
Minor
Inverse Problem

Cite this

Idowu, M. A., & Bown, J. L. (2012). Matrix operations for the simulation and immediate reverse-engineering of time series data. In D. Al-Dabass, A. Orsoni, & R. Cant (Eds.), Proceedings: 2012 14th International Conference on Modelling and Simulation (pp. 101-106). Piscataway, NJ: IEEE . https://doi.org/10.1109/UKSim.2012.24
Idowu, Michael A. ; Bown, James L. / Matrix operations for the simulation and immediate reverse-engineering of time series data. Proceedings: 2012 14th International Conference on Modelling and Simulation. editor / David Al-Dabass ; Alessandra Orsoni ; Richard Cant. Piscataway, NJ : IEEE , 2012. pp. 101-106
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abstract = "We present a new method for constructing and decomposing square matrices. This method, based on the computed parameterisation of their implied determinants and minors, operates on the product of factors of a new form of matrix decomposition. This method may be employed to build new matrices with fixed determinant(s). We demonstrate that this new approach is fundamentally well-connected to the Cholesky decomposition if applied on symmetric matrices. We also demonstrate that it is related to the LU decomposition method via a diagonal matrix multiplier. Also through this new method a direct relation between Cholesky decomposition and LU factorisation is shown. This method, presented for the first time, is useful for (re)constructing matrices with a predefined determinant and simulating inverse problems. The inference method introduced here also is based on new matrix manipulation techniques that we have developed for the identification of systems from reproducible time series data.",
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Idowu, MA & Bown, JL 2012, Matrix operations for the simulation and immediate reverse-engineering of time series data. in D Al-Dabass, A Orsoni & R Cant (eds), Proceedings: 2012 14th International Conference on Modelling and Simulation. IEEE , Piscataway, NJ, pp. 101-106, 14th International Conference on Computer Modelling and Simulation, Cambridge, United Kingdom, 28/03/12. https://doi.org/10.1109/UKSim.2012.24

Matrix operations for the simulation and immediate reverse-engineering of time series data. / Idowu, Michael A.; Bown, James L.

Proceedings: 2012 14th International Conference on Modelling and Simulation. ed. / David Al-Dabass; Alessandra Orsoni; Richard Cant. Piscataway, NJ : IEEE , 2012. p. 101-106.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - We present a new method for constructing and decomposing square matrices. This method, based on the computed parameterisation of their implied determinants and minors, operates on the product of factors of a new form of matrix decomposition. This method may be employed to build new matrices with fixed determinant(s). We demonstrate that this new approach is fundamentally well-connected to the Cholesky decomposition if applied on symmetric matrices. We also demonstrate that it is related to the LU decomposition method via a diagonal matrix multiplier. Also through this new method a direct relation between Cholesky decomposition and LU factorisation is shown. This method, presented for the first time, is useful for (re)constructing matrices with a predefined determinant and simulating inverse problems. The inference method introduced here also is based on new matrix manipulation techniques that we have developed for the identification of systems from reproducible time series data.

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Idowu MA, Bown JL. Matrix operations for the simulation and immediate reverse-engineering of time series data. In Al-Dabass D, Orsoni A, Cant R, editors, Proceedings: 2012 14th International Conference on Modelling and Simulation. Piscataway, NJ: IEEE . 2012. p. 101-106 https://doi.org/10.1109/UKSim.2012.24