Abstract
An \(M_\vee \)-matrix A has the form \(A=sI-B\), with B an eventually nonnegative matrix and \(s\ge \rho (B)\), the spectral radius of B. In this paper we study iterative procedures associated with a splitting of A, to solve the linear system \(Ax=b\), with the coefficient matrix A an \(M_\vee \)-matrix. We generalize the concepts of regular and weak regular splitting of a matrix using the notion of eventually nonnegative matrix , and term them as E-regular and weak E-regular splitting, respectively. We obtain necessary and sufficient conditions for the convergence of these types of splittings. We also discuss the convergence of Jacobi and Gauss-Seidel splittings for \(M_\vee \)-matrices.
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Acknowledgements
The author would like to express her gratitude to an anonymous referee for valuable suggestions and helpful comments. The author was supported by National Institute of Technology Meghalaya under Start-up grant.
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Saha, M. (2017). Iterative Method for Linear System with Coefficient Matrix as an \(M_\vee \)-matrix. In: Bebiano, N. (eds) Applied and Computational Matrix Analysis. MAT-TRIAD 2015. Springer Proceedings in Mathematics & Statistics, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-49984-0_16
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DOI: https://doi.org/10.1007/978-3-319-49984-0_16
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