A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors

Chu, Wei; Zhao, Yong; Yuan, Hua

doi:10.3390/math10193636

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…Caratelli and Ricci (2021) presented method for inverting non-singular tridiagonal matrices using a classic functional analysis tool: Dunford-Taylor's integral, which adds operators to Cauchy's integral formula. Chu et al (2022) proposed a modified inverse iteration method for computing symmetric tridiagonal eigenvectors. Hopkins and Kilic (2022) presented an algorithm for determining the inverse and the determinant of an extended, periodic, tridiagonal 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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Section: Introductionmentioning

confidence: 99%

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Thirupathi,

Thamaraiselvan

2024

Sci. Technol. Indones

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A Novel Finite Difference Scheme for Normal Mode Models in Underwater Acoustics

Liu

Cheng

et al. 2023

JMSE

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Normal mode models are commonly used to simulate sound propagation problems in horizontally stratified oceanic environments. Although several normal mode models have been developed, the fundamental techniques for accurately and efficiently solving the modal equation are still under development. Since the standard three-point central finite difference scheme (SFD) for the modal equation has a relatively large numerical error, at least twenty sampling grid points per wavelength should be set in the depth direction. Herein, a novel finite difference scheme (NFD) is developed to further improve the accuracy of the mode solution, and the resulting linear system still has a tridiagonal structure similar to that of the SFD. To compare the performance of the NFD to that of the SFD, the NFD has been implemented in the open-source normal mode model KrakenC, and three acoustic propagation cases have been carried out, including the plane-wave reflection, the Pekeris waveguide, and the Munk waveguide. Test results show that the NFD presented in this paper is more accurate than the SFD, and can be used to reduce the number of grid points needed in the depth direction for solving the modal equation in normal mode models.

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A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors

Cited by 2 publications

References 17 publications

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

A Novel Finite Difference Scheme for Normal Mode Models in Underwater Acoustics

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