Iterative methods for solving absolute value equations

Ali, Rashid; Ali, Azmat; Iqbal, S.

doi:10.22436/jmcs.026.04.01

Cited by 16 publications

(7 citation statements)

References 32 publications

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“…Theorem 3. If either of the following conditions satisfy then GAVE (1) has exactly one solution for each b: (i) [19] σ max (|B|) < σ min (A); (ii) [24] 2 2 I n is a positive definite matrix.…”

Section: Lemma 1 [7]mentioning

confidence: 99%

A Note on Unique Solvability of the Generalized Absolute Value Matrix Equation

Kumar

Deepmala

2023

Natl. Acad. Sci. Lett.

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In this survey paper, we focus on the necessary and sufficient conditions for the unique solvability and unsolvability of the absolute value equations (AVEs) during the last twenty years (2004 to 2023). We discussed unique solvability conditions for various types of AVEs like standard absolute value equation (AVE), Generalized AVE (GAVE), New generalized AVE (NGAVE), Triple AVE (TAVE) and a class of NGAVE based on interval matrix, P-matrix, singular value conditions, spectral radius and W-property. Based on unique solution of AVEs, we also discussed unique solvability conditions for linear complementarity problems (LCP) and horizontal linear complementarity problems (HLCP).

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Section: Lemma 1 [7]mentioning

confidence: 99%

A Note on Unique Solvability of the Generalized Absolute Value Matrix Equation

Kumar

Deepmala

2023

Natl. Acad. Sci. Lett.

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“…Elzaki transform (ET) is an integral transform [22] in this context. Several scholars [23][24][25][26][27][28][29][30] have looked at some essential solution approaches for real-world issues, as well as numerical simulations obtained using the novel integral transformation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform

Shah

El‐Zahar

Akgül

et al. 2022

Journal of Function Spaces

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A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new technique combining integral transformation, the Elzaki transform (ET), and apply it to regularized long-wave equations in this study. The RLW equations describe ion-acoustic waves in plasma and shallow water waves in seas. The results obtained are extremely important and necessary for describing various physical phenomena. This work considers an up-to-date approach and fractional operators in this context to obtain satisfactory approximate solutions to the proposed problems. We first define the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD) and implement them for solving RLW equations. We can readily obtain numerical results that provide us with improved approximations after only a few iterations. The derived solutions were found to be in close contact with the exact solutions. Furthermore, the suggested procedure has attained the best level of accuracy. In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.

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“…Chen et al [16] showed the SOR-like strategy with optimal parameters and examined some novel convergence situations different from [15]. Zamani and Hladík [17] offered a new concave minimization approach for AVE (1), which addresses the deficiency of the system proposed in [18] and others (see [19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%