Computational algorithms for computing the inverse of a square matrix, quasi-inverse of a non-square matrix and block matrices

Najafi, H. Saberi; Solary, Maryam Shams

doi:10.1016/j.amc.2006.05.108

Cited by 22 publications

(6 citation statements)

References 5 publications

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“…Capacitances and resistance L s ¼ 0:431 requiring the calculation of per-section series impedances Z s1 , Z s2 , …, Z s6 using (32). To compute these impedances, the parameter matrices R, L, C, and K are determined using (24) and (31). By substituting these matrices, along with the variables, into (32), the per-section series impedances can be obtained.…”

Section: Inductances (Mh)mentioning

confidence: 99%

“…To derive symbolic expressions for V ðsÞ and IðsÞ, it is essential to compute the inverse of the characteristic polynomial sI À A ð Þ. However, this task becomes challenging and complex due to the presence of the symbolic variable s. To address this challenge, the block matrix inversion method 31 is employed, allowing the calculation of the polynomial inverse block by block. The process is carried out as follows:…”

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confidence: 99%

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Analytical computation of driving point impedance in mutually coupled inhomogeneous ladder networks

Lakshmi Prasanna,

Mondal

2023

Circuit Theory & Apps

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SummaryElectrical systems are traditionally modeled as homogeneous ladder networks, disregarding the inherent inhomogeneity found in real‐world systems. This can result in inaccuracies in analysis and design. The driving point impedance (DPI) is a crucial parameter for studying electrical systems, as it can be conveniently measured at the terminals. However, existing methods for calculating DPI have limitations, including increased complexity, high computational demands, convergence issues, and challenges in capturing high‐frequency effects. A new approach for computing DPI of inhomogeneous ladder networks, reducible to series and shunt impedance circuit form, is introduced in this research. The method is based on state‐space formulations and projective matrix analysis. It offers improved accuracy as compared with existing methods and can be applied to a wide range of networks. Simulation results from a six‐section mutually coupled inhomogeneous ladder network validate the effectiveness of the proposed approach. This research addresses the disregarded factors of inhomogeneity and mutual coupling within traditional approaches, presenting a significant advancement in the analysis and design of electrical systems.

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Section: Inductances (Mh)mentioning

confidence: 99%

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confidence: 99%

Analytical computation of driving point impedance in mutually coupled inhomogeneous ladder networks

Lakshmi Prasanna,

Mondal

2023

Circuit Theory & Apps

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“…In this paper, we demonstrate that significant reductions in computational time can be achieved by applying to EEIOA a theorem first proved by Woodbury in 1950 (Woodbury, 1950). Other authors have investigated the use of matrix partitioning and the Sherman–Morrison formula (a special case of the Woodbury formula for a single row or column update) for various applications (Chen et al., 2018; Lai & Vemuri, 1997; Saberi Najafi & Shams Solary, 2006), including Miller and Blair (Miller & Blair, 2009). However, the focus of the former works is not applicable because of their specificity to other scientific fields, while the latter concerns the study of effects of single changes or error in the data, and does not include formulas for multiple changes or errors.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of environmentally extended input–output scenario and circular economy modeling

Çetinay

Donati

Heijungs

et al. 2020

J of Industrial Ecology

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Industrial ecology tools are increasingly being used in ways that require high computational times. In the policy arena, this becomes problematic when practitioners want to live-test various alternatives in a responsive and web-based platform. In research, computational times come into play when analyzing large systems with multiple interventions or when requiring many runs for, for example, Monte Carlo simulations. We demonstrate how the computational time of a number of commonly used industrial ecology tools can be reduced significantly, potentially by multiple orders of magnitude. Our case study was the optimization of scenario calculations in Environmentally Extended Input-Output Analysis (EEIOA). Instead of recalculating the Leontief inverse after individual changes to the interindustry relations, as is done traditionally in EEIOA scenario analysis, we give formulations to find the total value of the change in the environmental indicators in one calculation step. We illustrate these novel formulations both for a simple hypothetical system and for the full EXIOBASE EEIO model. The use of explicit formulas decreases the computational time to the degree that it becomes possible to carry out these analyses in live or web-based environments. For our case study, we find an improvement of up to four orders of magnitude.

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“…where I n is the identity matrix, and X 0 is an initial value for approximating A −1 . This iterative method will quadratically converge to A −1 , after enough iterations provided that all eigenvalues of I n − X 0 A are less than 1, i.e., for a matrix norm it holds that I n − X 0 A < 1 [6].…”

Section: Introductionmentioning

confidence: 99%

A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse

Kokabifar

2020

Communications in Advanced Mathematical Sciences

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In this work, a family of iterative algorithms for approximating the inverse of a square matrix and the Moore-Penrose inverse of a non-square one is proposed. These methods are based on arbitrary high-order iterative techniques which are used for computing roots of a nonlinear function. Therefore the presented techniques occupy any high-order convergence. The proposed methods are convenient and self-explanatory, achieve satisfactory results, and also require less and easy computations compared to some current schemes. Experimental results are provided to illustrate the reliability and robustness of the techniques.

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Computational algorithms for computing the inverse of a square matrix, quasi-inverse of a non-square matrix and block matrices

Cited by 22 publications

References 5 publications

Analytical computation of driving point impedance in mutually coupled inhomogeneous ladder networks

Analytical computation of driving point impedance in mutually coupled inhomogeneous ladder networks

Efficient computation of environmentally extended input–output scenario and circular economy modeling

A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse

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