Schur Complement-Based Infinity Norm Bounds for the Inverse of SDD Matrices

Li, Chaoqian

doi:10.1007/s40840-020-00895-x

Cited by 14 publications

(2 citation statements)

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“…In addition, many researchers obtained other results for the smallest singular value; see [11,13,24] and references therein. Based on Theorem 7, a new lower bound for σ n (A) is obtained.…”

Section: Applications To the Smallest Singular Value For Dzt Matrixmentioning

confidence: 99%

“…A traditional approach to finding upper bounds for the infinity norm of the inverse of nonsingular matrices involves utilizing the definition and properties of a given matrix class. For further details, please refer to [8][9][10][11][12][13]. This work has its origins in 1975 when Varah [14] proposed a straightforward and refined upper bound for the infinity norm of the inverse of the strictly diagonally dominant (SDD) matrices class, which is one of the most vital subclasses of H-matrices.…”

Section: Introductionmentioning

confidence: 99%

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Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices

Zeng

Liu

2023

Mathematics

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It is necessary to explore more accurate estimates of the infinity norm of the inverse of a matrix in both theoretical analysis and practical applications. This paper focuses on obtaining a tighter upper bound on the infinite norm of the inverse of Dashnic–Zusmanovich-type (DZT) matrices. The realization of this goal benefits from constructing the scaling matrix of DZT matrices and the diagonal dominant degrees of Schur complements of DZT matrices. The effectiveness and superiority of the obtained bounds are demonstrated through several numerical examples involving random variables. Moreover, a lower bound for the smallest singular value is given by using the proposed bound.

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Section: Applications To the Smallest Singular Value For Dzt Matrixmentioning

confidence: 99%