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Diagonal dominance, Schur complements and some classes of H-matrices and P-matrices

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Abstract

We analyze a class of matrices generalizing strictly diagonally dominant matrices and included in the important class of H-matrices. Adequate pivoting strategies and the corresponding Schur complements are studied. A new class of matrices with all their principal minors positive is presented.

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References

  1. Alanelli, M., Hadjidimos, A.: A new iterative criterion for H-matrices. SIAM J. Matrix Anal. Appl. 29, 160–176 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alanelli, M., Hadjidimos, A.: On iterative criteria for H-and non-H-matrices. Appl. Math. Comput. 188, 19–30 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alanelli, M., Hadjidimos, A.: A new iterative criterion for H-matrices: the reducible case. Linear Algebra Appl. 428, 2761–2777 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. In: Classics in Applied Mathematics, vol. 9. SIAM, Philadelphia (1994)

    Google Scholar 

  5. Bru, R., Corral, C., Gimenez, I., Mas, J.: Classes of general H-matrices. Linear Algebra Appl. 429, 2358–2366 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cvetković, L., Kostić, V., Kovaćević, M., Szulc, T.: Further results on H-matrices and their Schur complements. Appl. Math. Comput. 198, 506–510 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cvetković, L., Nedović, M.: Special H-matrices and their Schur and diagonal-Schur complements. Appl. Math. Comput. 208, 225–230 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gudkov, V.V.: On a certain test for non-singularity of matrices (Russian). In: Latvian Math. Yearbook. Izdat. “Zinatne”, pp. 385–390. Riga (1965), (MR 33, 1966, #1323)

  9. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)

    MATH  Google Scholar 

  10. Kohno, T., Niki, H., Sawami, H., Gao, Y.: An iterative test for H-matrices. J. Comput. Appl. Math. 115, 349–355 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, B., Li, L., Harada, M., Niki, H., Tsatsomeros, M.J.: An iterative criterion for H-matrices. Linear Algebra Appl. 271, 79–190 (1998)

    MathSciNet  Google Scholar 

  12. Ojiro, K., Niki, H., Usui, M.: A new criterion for H-matrices. J. Comput. Appl. Math. 150, 293–302 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peña, J.M.: Pivoting strategies leading to diagonal dominance by rows. Numer. Math. 81, 293–304 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Peña, J.M.: A class of P-matrices with applications to the localization of the eigenvalues of a real matrix. SIAM J. Matrix Anal. Appl. 22, 1027–1037 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Peña, J.M.: Scaled pivots and scaled partial pivoting strategies. SIAM J. Numer. Anal. 41, 1022–1031 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Peña, J.M.: On an alternative to Gerschgorin circles and ovals of Cassini. Numer. Math. 95, 337–345 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Peña, J.M.: A stable test to check if a matrix is a nonsingular M-matrix. Math. Comput. 73, 1385–1392 (2004)

    Article  MATH  Google Scholar 

  18. Szulc, T.: Some remark is on a theorem of Gudkov. Linear Algebra Appl. 225, 221–235 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Juan Manuel Peña

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  1. Juan Manuel Peña
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Correspondence to Juan Manuel Peña.

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Communicated by Guest editors Juan Manuel Peña and Rafael Bru.

Research partially supported the Spanish Research Grant MTM2009-07315, Gobierno de Aragón and Fondo Social Europeo.

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Peña, J.M. Diagonal dominance, Schur complements and some classes of H-matrices and P-matrices. Adv Comput Math 35, 357–373 (2011). https://doi.org/10.1007/s10444-010-9160-5

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  • DOI: https://doi.org/10.1007/s10444-010-9160-5

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