The Determinant of an Interval Matrix Using Gaussian Elimination Method

Nirmala, T.; Datta, Debabrata; Kushwaha, H.S.; Ganesan, K.

doi:10.12732/ijpam.v88i1.2

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…The system is evaluated by three mathematical formulations which were developed by Gauss, Krawski and Hansen (Nirmala et al, 2013;Hansen and Sengupta, 1981;Neumaier, 1999). To avoid possible rounding errors and divergent results, we propose to use an intersection method.…”

Section: Calculation Of Unknown Displacementsmentioning

confidence: 99%

Consideration of the uncertainty in the dimensioning of a gearbox of a wind turbine

Trabelsi¹,

Guizani²,

Barkallah³

et al. 2020

Journal of Theoretical and Applied Mechanics

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The paper deals with the design approach of a subdefinite mechatronic system and focuses on the sizing stage of a gearbox of a wind turbine based on the interval computation method. Indeed, gearbox design variables are expressed by intervals to take into account the uncertainty in the estimation of these parameters. The application of the interval computation method allows minimizing the number of simulations and enables obtaining a set of solutions instead of a single one. The dynamic behavior of the gearbox is obtained using the finite element method. The challenge here is to get convergent results with intervals that reflect the efficiency of the applied method. Thus, several mathematical formulations have been tested in static study and evaluated in the case of a truss. Then the interval computation method was used to simulate the behavior of the wind turbine gearbox.

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Section: Calculation Of Unknown Displacementsmentioning

confidence: 99%

Consideration of the uncertainty in the dimensioning of a gearbox of a wind turbine

Trabelsi¹,

Guizani²,

Barkallah³

et al. 2020

Journal of Theoretical and Applied Mechanics

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show abstract

“…Ganesan and Veeramani (2005) developed an innovative collection of arithmetic operations for interval numbers with the overarching goal of mitigating disparities in a general context. Nirmala et al (2011) devised an inventive approach for calculating the inverse of an interval matrix, which subsequently proved to be a valuable tool for addressing interval-linear problems. Hartman et al (2021) introduced an algorithm for computing the spectral decomposition of an interval matrix.…”

Section: Introductionmentioning

confidence: 99%

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Thirupathi,

Thamaraiselvan

2024

Sci. Technol. Indones

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Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

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“…Ganesan and Veeramani(2005) offered some properties on interval matrices. Nirmala et al(2011) studied a new approach on inverse interval matrix. Sudha et al(2021) suggested a novel method for handling fixed charge transportation issues using interval parameters.…”

Section: Introductionmentioning

confidence: 99%

A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems

Ganesan,

2023

Pak.j.stat.oper.res.

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The objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given.

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The Determinant of an Interval Matrix Using Gaussian Elimination Method

Abstract: We introduce the notion of determinant and related results for interval matrices. We propose a Gaussian elimination like algorithm for computing the enclosures of the determinant of interval matrices. Numerical examples are also provided to show the efficiency of the proposed algorithm.

Cited by 8 publications

References 16 publications

Consideration of the uncertainty in the dimensioning of a gearbox of a wind turbine

Consideration of the uncertainty in the dimensioning of a gearbox of a wind turbine

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems

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