Criteria for α-Diagonally Dominant Matrices and its Applications

Qi Chen; Min Li

doi:10.4028/www.scientific.net/AMM.380-384.1346

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 380-384Criteria for α-Diagonally Dominant Matrices and...

Criteria for α-Diagonally Dominant Matrices and its Applications

Abstract:

How to check if a given matrix is a nonsingular matrix is important. In the recent paper, several simple criteria, as well as a necessary condition for nonsingular matrices, have been obtained. Inspired by these results, we partition the row and column index set of square matrix, construct a positive diagonal matrix according to the elements and row sum, column sum of the matrix as well, then obtain a new criterion for the nonsingular matrices, and extend the criteria of nonsingular matrices. Finally, a numerical example for the effectiveness of the proposed criterion is presented.

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Periodical:

Applied Mechanics and Materials (Volumes 380-384)

Pages:

1346-1349

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.380-384.1346

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Online since:

August 2013

Authors:

Qi Chen, Min Li

Keywords:

Diagonally Dominant Matrices, α-Diagonallydominant Matrices, Η-Matrices

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References

[1] A Berman and R.J. Plemmons. Nonnegative Matrices in the Mathematical Sciences, SIAM Press, Philadelphia, (1994).

Google Scholar

[2] R.S. Varga, On Recurring Theorems on Diagonal Dominance, Linear Algebra Appl. 1976. 1-9.

Google Scholar

[3] J. Wang, Z. Xu and Q. Lu. A Set of New Criteria Conditions for Generalized Strictly Diagonally Dominany Matrices, Mathematica Numerica Sinica[J]. 2011(33) 225-232.

Google Scholar

[4] R. Jiang. New Criteria for Nonsingular matrix, Chinese Journal of Engineering Mathematics[J]. 2011(28) 393-400.

Google Scholar

[5] C.Y. Leng. Criteria for Nonsingular matrix, Acta Mathematicae Applicatae Sinica[J]. 2011(34) 50-56.

Google Scholar

[6] M. Li and Y.X. Sun. Discussion for diagonally Dominant Matrices and its Applications, Chinese Journal of Engineering Mathematics[J]. 2009(26) 941-945.

Google Scholar

[7] T.B. Gan and T.Z. Huang. Simple Criteria for Nonsingular matrix, Linear Algebra Appl[J]. 2003. 317-326.

Google Scholar

[8] M. Li and Y.X. Sun. Practical Criteria for matrices, Applied Mathematics and Computation[J]. 2009(211) 427-433.

DOI: 10.1016/j.amc.2009.01.083

Google Scholar

[9] X.F. Fang and T.Z. Huang. Connective Diagonally Dominant Matrices and matrices, Chinese Journal of Engineering Mathematics[J]. 2005(22) 123-127.

Google Scholar

[10] M. Li and Q.C. Li. New Criteria for Nonsingular matrices, Chinese Journal of Engineering Mathematics[J]. 2012(29) 715-719.

Google Scholar

[11] Q. Chen and M. Li. Criteria for Nonsingular matrices, Computer Science and Electronics Engineering, 2013(2) 582-585.

Google Scholar