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On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials
Index-proper nonnegative splittings of matrices
1. | Department of Mathematics, National Institute of Technology Raipur, Raipur - 492 010, India |
References:
[1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4612-0873-0. |
[2] |
A. K. Baliarsingh and L. Jena, A note on index-proper multisplittings of matrices, Banach J. Math. Anal., 9 (2015), 384-394.
doi: 10.15352/bjma/09-4-19. |
[3] |
A. K. Baliarsingh and D. Mishra, Comparison results for proper nonnegative splittings of matrices, Results. Math., online, 2015.
doi: 10.1007/s00025-015-0504-9. |
[4] |
A. Berman and R. J. Plemmons, Cones and iterative methods for best square least squares solutions of linear systems, SIAM J. Numer. Anal., 11 (1974), 145-154. |
[5] |
L. Jena, Extensions of regular and weak regular splittings to real square singular matrices, submitted. |
[6] |
L. Jena and D. Mishra, BD-splittings of matrices, Linear Algebra Appl., 437 (2012), 1162-1173.
doi: 10.1016/j.laa.2012.04.009. |
[7] |
L. Jena and S. Pani, Index-range monotonicity and index proper splittings of matrices, Numer. Algebra Control Optim, 3 (2013), 379-388.
doi: 10.3934/naco.2013.3.379. |
[8] |
L. Jena, D. Mishra and S. Pani, Convergence and comparisons of single and double decompositions of rectangular matrices, Calcolo, 51 (2014), 141-149.
doi: 10.1007/s10092-013-0079-3. |
[9] |
I. Marek and D. B. Szyld, Comparison theorems for weak splittings of bounded operators, Numer. Math., 58 (1990), 387-397.
doi: 10.1007/BF01385632. |
[10] |
D. Mishra, Nonnegative splittings for rectangular matrices, Comput. Math. Appl., 67 (2014), 136-144.
doi: 10.1016/j.camwa.2013.10.012. |
[11] |
S. Q. Shen and T. Z. Huang, Convergence and comparison theorems for double splittings of matrices, Comput. Math. Appl., 51 (2006), 1751-1760.
doi: 10.1016/j.camwa.2006.02.006. |
[12] |
Y. Song, Comparison theorems for splittings of matrices, Numer. Math., 92 (2002), 563-591.
doi: 10.1007/s002110100333. |
[13] |
R. S. Varga, Matrix Iterative Analysis, Springer-Verlag, Berlin, 2000.
doi: 10.1007/978-1-4612-0873-0. |
[14] |
Y. Wei, Index splitting for the Drazin inverse and the singular linear system, Appl. Math. Comput., 95 (1998), 115-124.
doi: 10.1016/S0096-3003(97)10098-4. |
show all references
References:
[1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4612-0873-0. |
[2] |
A. K. Baliarsingh and L. Jena, A note on index-proper multisplittings of matrices, Banach J. Math. Anal., 9 (2015), 384-394.
doi: 10.15352/bjma/09-4-19. |
[3] |
A. K. Baliarsingh and D. Mishra, Comparison results for proper nonnegative splittings of matrices, Results. Math., online, 2015.
doi: 10.1007/s00025-015-0504-9. |
[4] |
A. Berman and R. J. Plemmons, Cones and iterative methods for best square least squares solutions of linear systems, SIAM J. Numer. Anal., 11 (1974), 145-154. |
[5] |
L. Jena, Extensions of regular and weak regular splittings to real square singular matrices, submitted. |
[6] |
L. Jena and D. Mishra, BD-splittings of matrices, Linear Algebra Appl., 437 (2012), 1162-1173.
doi: 10.1016/j.laa.2012.04.009. |
[7] |
L. Jena and S. Pani, Index-range monotonicity and index proper splittings of matrices, Numer. Algebra Control Optim, 3 (2013), 379-388.
doi: 10.3934/naco.2013.3.379. |
[8] |
L. Jena, D. Mishra and S. Pani, Convergence and comparisons of single and double decompositions of rectangular matrices, Calcolo, 51 (2014), 141-149.
doi: 10.1007/s10092-013-0079-3. |
[9] |
I. Marek and D. B. Szyld, Comparison theorems for weak splittings of bounded operators, Numer. Math., 58 (1990), 387-397.
doi: 10.1007/BF01385632. |
[10] |
D. Mishra, Nonnegative splittings for rectangular matrices, Comput. Math. Appl., 67 (2014), 136-144.
doi: 10.1016/j.camwa.2013.10.012. |
[11] |
S. Q. Shen and T. Z. Huang, Convergence and comparison theorems for double splittings of matrices, Comput. Math. Appl., 51 (2006), 1751-1760.
doi: 10.1016/j.camwa.2006.02.006. |
[12] |
Y. Song, Comparison theorems for splittings of matrices, Numer. Math., 92 (2002), 563-591.
doi: 10.1007/s002110100333. |
[13] |
R. S. Varga, Matrix Iterative Analysis, Springer-Verlag, Berlin, 2000.
doi: 10.1007/978-1-4612-0873-0. |
[14] |
Y. Wei, Index splitting for the Drazin inverse and the singular linear system, Appl. Math. Comput., 95 (1998), 115-124.
doi: 10.1016/S0096-3003(97)10098-4. |
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