More on proper nonnegative splittings of rectangular matrices. (English) Zbl 1487.15006
Summary: In this paper, we further investigate the single proper nonnegative splittings and double proper nonnegative splittings of rectangular matrices. Two convergence theorems for the single proper nonnegative splitting of a semimonotone matrix are derived, and more comparison results for the spectral radii of matrices arising from the single proper nonnegative splittings and double proper nonnegative splittings of different rectangular matrices are presented. The obtained results generalize the previous ones, and it can be regarded as the useful supplement of the results in [D. Mishra, Comput. Math. Appl. 67, No. 1, 136–144 (2014; Zbl 1350.65025); A. K. Baliarsingh and D. Mishra, Result. Math. 71, No. 1–2, 93–109 (2017; Zbl 1360.65097)].
MSC:
| 15A06 | Linear equations (linear algebraic aspects) |
| 15A09 | Theory of matrix inversion and generalized inverses |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65F10 | Iterative numerical methods for linear systems |
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
Keywords:
rectangular matrix; proper nonnegative splitting; convergence; comparison theorems; Moore-Penrose inverseReferences:
| [1] | K, Comparison results for proper double splittings of rectangular matrices, Filomat, 32, 2273-2281 (2018) · Zbl 1499.15006 |
| [2] | A. Ben-Israel, T. N. E. Greville, <i>Generalized Inverses. Theory and Applications</i>, Springer, New York, 2003. · Zbl 1026.15004 |
| [3] | A, Comparison results for proper nonnegative splittings of matrices, Results Math., 71, 93-109 (2017) · Zbl 1360.65097 |
| [4] | A, Cones and iterative methods for best squares least square solution of linear systems, SIAM J. Numer. Anal., 11, 145-154 (1974) · Zbl 0244.65024 |
| [5] | A. Berman, R. J. Plemmons, <i>Nonnegative Matrices in the Mathematical Sciences</i>, SIAM, Philadelphia, 1994. · Zbl 0815.15016 |
| [6] | J.-J. Climent, A. Devesa, C. Perea, Convergence results for proper splittings, <i>Recent Advances in</i> <i>Applied and Theoretical Mathematics</i>, (2000), 39-44. · Zbl 1043.65061 |
| [7] | J, Iterative methods for least squares problems based on proper splittings, J. Comput. Appl. Math., 158, 43-48 (2003) · Zbl 1033.65021 |
| [8] | L, Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices, Linear Algebra Appl., 363, 65-80 (2003) · Zbl 1018.65049 |
| [9] | L, Convergence and comparison theorems for single and double decompositions of rectangular matrices, Calcolo, 51, 141-149 (2014) · Zbl 1318.65017 |
| [10] | S, Comparison theorems for nonnegative double splittings of different monotone matrices, J. Inf. Comput. Math. Sci., 9, 1421-1428 (2012) |
| [11] | D, Nonnegative splittings for rectangular matrices, Comput. Math. Appl., 67, 136-144 (2014) · Zbl 1350.65025 |
| [12] | S, On comparison theorems for splittings of different semimonotone matrices, J. Appl. Math., 2014, 329490 (2014) · Zbl 1442.65046 |
| [13] | N, Two-stage iterations based on composite splittings for rectangular linear systems, Comput. Math. Appl., 75, 2746-2756 (2018) · Zbl 1415.65079 |
| [14] | D, Comparison theorems for a subclass of proper splittings of matrices, Appl. Math. Lett., 25, 2339-2343 (2012) · Zbl 1252.65069 |
| [15] | S, A note on double splittings of different matrices, Calcolo, 46, 261-266 (2009) · Zbl 1185.65058 |
| [16] | V. Shekhar, C. K. Giri, D. Mishra, A note on double weak splittings of type II, <i>Linear Multilinear</i> <i>Algebra</i>, (2020), 1-21. |
| [17] | S, Convergence and comparison theorems for double splittings of matrices, Comput. Math. Appl., 51, 1751-1760 (2006) · Zbl 1134.65341 |
| [18] | J, Convergence for nonnegative double splittings of matrices, Calcolo, 48, 245-260 (2011) · Zbl 1232.65056 |
| [19] | Z, Estimation of the optimum relaxation factors in partial factorization iterative methods, SIAM J. Matrix Anal. Appl., 13, 59-73 (1993) · Zbl 0767.65025 |
| [20] | G. Wang, Y. Wei, S. Qiao, <i>Generalized Inverses: Theory and Computations</i>, Science Press, Beijing, 2004. |
| [21] | R. S. Varga, <i>Matrix Iterative Analysis</i>, Springer, Berlin, 2000. · Zbl 0998.65505 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
