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Scaling technique for Partition-Nekrasov matrices

Author

Listed:
  • Szulc, Tomasz
  • Cvetković, Ljiljana
  • Nedović, Maja

Abstract

It is well-known that for a given H-matrix A there exists a diagonal nonsingular matrix that scales A (by multiplying it from the right) to a strictly diagonally dominant (SDD) matrix. There are subclasses of H-matrices that can be fully characterised by the form of the corresponding diagonal scaling matrices. However, for some applications, it is not necessary to have such full characterisation. It is sufficient to find at least one scaling matrix that will do the job. The aim of this paper is to present a way of constructing a diagonal scaling matrix for one special subclass of H-matrices called Partition-Nekrasov matrices. As an application of this scaling approach, we obtain eigenvalue localisation for the corresponding Schur complement matrix, using only the entries of the original matrix.

Suggested Citation

  • Szulc, Tomasz & Cvetković, Ljiljana & Nedović, Maja, 2015. "Scaling technique for Partition-Nekrasov matrices," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 201-208.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:201-208
    DOI: 10.1016/j.amc.2015.08.136
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    Cited by:

    1. Orera, H. & Peña, J.M., 2019. "Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 119-127.

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