publication . Preprint . 2014

Iterative methods for the inclusion of the inverse matrix

Petkovic, Marko D.; Petkovic, Miodrag S.;
Open Access English
  • Published: 20 Jun 2014
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval iterations. The new method is relied on a suitable matrix identity and a modification of a hyper-power method. This method is also feasible in the case of a full-rank $m\times n$ matrix, producing the interval sequence which converges to the Moore-Penrose inverse. It is shown that computational efficiency of the proposed method is equal or higher than the methods of hyper-power's type.
free text keywords: Mathematics - Numerical Analysis, 15A09, 65G30, 47J25, 03D15, 65H05
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MESTD| Graph theory and mathematical programming with applications in chemistry and computer science
  • Funder: Ministry of Education, Science and Technological Development of Republic of Serbia (MESTD)
  • Project Code: 174033
  • Funding stream: Basic Research (BR or ON)
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[1] G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983.

[2] R. Brent, P. Zimmermann, Modern Computer Arithmetic, Cambridge University Press, Cambridge, 2011.

[3] R. E. Moore, R. B. Kearfott, M. J. Cloud, Introduction to Interval Analysis, SIAM, Philadelphia, 2009.

[4] M.S. Petkovi´c, Iterative Methods for Simultaneous Inclusion of Polynomial Zeros, Springer-Verlag, Berlin-Heidelberg-New York, 1989.

[5] M.S. Petkovi´c, J. Herzberger, On the efficiency of a class of combined Schulz's method for bounding the inverse matrix, ZAMM 71 (1991), 181-187.

[6] M. S. Petkovi´c, L. D. Petkovi´c, Complex Interval Arithmetic and its Applications, Wiley-VCH, Berlin-Weinheim-New York, 1998.

[7] X. Zhang, J. Cai, Y. Wei, Interval iterative methods for computing Moore-Penrose inverse, Appl. Math. Comput 183 (2006), 522-532.

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