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Continued fraction expansions of some functions of positive definite matrices

Year 2013, Volume: 1 Issue: 1, 49 - 54, 01.04.2013

Ali Kacha Brahim Ounir Brahim Moalige

https://izlik.org/JA44AK87GN

Abstract

In this paper we recall some results of matrix functions with eal cofficients. The aim of this paper is to provide some properties and results of continued fractions with matrix arguments. Then we give continued fractions expansions of some inverse of hyperbolic and circular functions and where is a positive definite matrix

Keywords

Continued fraction expansion positive definite matrix function of matrices

References

  • T.Ando, Topics on operators inequalities, Ryukyu Univ. Lecture Note Series, 1 (1978).
  • S. M. Cox & P. C. Matthews: Exponential time diferencing for sti_ systems. J. Comp. Phys., 176 (2); 430-455, 2002.
  • A. Cuyt & V. Brevik Petersen, Handbook of continued fractions for special functions, Springer (2007).
  • F. R. Gantmacher: The Theory of Matrices, Vol. I. Chelsa, New York, 1959. Elsevier Science Publishers, (1992).
  • V. Gen H. Golub & Charles F. Van Loan: Matrix Computations, Johns Hopking University Press, Baltimore, MD, USA, third edition, (1996).
  • W.B.Jons & W.J. Thron: Continued Fractions, Analytic Theory and Applications, Addison-Westly Publishing Company, 5. (1980).
  • Peter Lancaster & Miron Tismenetsky. The Theory of Matrices. Academic Press, New York, second editions, (1985).
  • L.Lorentzen, H.Wadeland, Continued fractions with application, Elseiver Science Publishers, (1992).
  • M.Raissouli & A.Kacha, Convergence for matrix continued fractions, Linear Algebra and its Applications, bf 320 (2000), pp.115-129.
  • M.Raissouli & F.Leazizi, Continued fractions expansion of the geometric matrix means and applications, Linear Algebra and its Appl, 359 (2003), pp. 37-57.
  • R.S.Varga, On higher order stable implicit methods for solving parabolic partial diferential equations, J. Math. Phys, 40 (1961), pp. 220-231.

CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES

Year 2013, Volume: 1 Issue: 1, 49 - 54, 01.04.2013

Ali Kacha Brahim Ounir Brahim Moalige

https://izlik.org/JA44AK87GN

Abstract

References

  • T.Ando, Topics on operators inequalities, Ryukyu Univ. Lecture Note Series, 1 (1978).
  • S. M. Cox & P. C. Matthews: Exponential time diferencing for sti_ systems. J. Comp. Phys., 176 (2); 430-455, 2002.
  • A. Cuyt & V. Brevik Petersen, Handbook of continued fractions for special functions, Springer (2007).
  • F. R. Gantmacher: The Theory of Matrices, Vol. I. Chelsa, New York, 1959. Elsevier Science Publishers, (1992).
  • V. Gen H. Golub & Charles F. Van Loan: Matrix Computations, Johns Hopking University Press, Baltimore, MD, USA, third edition, (1996).
  • W.B.Jons & W.J. Thron: Continued Fractions, Analytic Theory and Applications, Addison-Westly Publishing Company, 5. (1980).
  • Peter Lancaster & Miron Tismenetsky. The Theory of Matrices. Academic Press, New York, second editions, (1985).
  • L.Lorentzen, H.Wadeland, Continued fractions with application, Elseiver Science Publishers, (1992).
  • M.Raissouli & A.Kacha, Convergence for matrix continued fractions, Linear Algebra and its Applications, bf 320 (2000), pp.115-129.
  • M.Raissouli & F.Leazizi, Continued fractions expansion of the geometric matrix means and applications, Linear Algebra and its Appl, 359 (2003), pp. 37-57.
  • R.S.Varga, On higher order stable implicit methods for solving parabolic partial diferential equations, J. Math. Phys, 40 (1961), pp. 220-231.
There are 11 citations in total.

Details

Authors

Ali Kacha This is me

Brahim Ounir This is me

Brahim Moalige This is me

Publication Date April 1, 2013
IZ https://izlik.org/JA44AK87GN
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

APA Kacha, A., Ounir, B., & Moalige, B. (2013). CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES. New Trends in Mathematical Sciences, 1(1), 49-54. https://izlik.org/JA44AK87GN
AMA 1.Kacha A, Ounir B, Moalige B. CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES. New Trends in Mathematical Sciences. 2013;1(1):49-54. https://izlik.org/JA44AK87GN
Chicago Kacha, Ali, Brahim Ounir, and Brahim Moalige. 2013. “CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES”. New Trends in Mathematical Sciences 1 (1): 49-54. https://izlik.org/JA44AK87GN.
EndNote Kacha A, Ounir B, Moalige B (April 1, 2013) CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES. New Trends in Mathematical Sciences 1 1 49–54.
IEEE [1]A. Kacha, B. Ounir, and B. Moalige, “CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES”, New Trends in Mathematical Sciences, vol. 1, no. 1, pp. 49–54, Apr. 2013, [Online]. Available: https://izlik.org/JA44AK87GN
ISNAD Kacha, Ali - Ounir, Brahim - Moalige, Brahim. “CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES”. New Trends in Mathematical Sciences 1/1 (April 1, 2013): 49-54. https://izlik.org/JA44AK87GN.
JAMA 1.Kacha A, Ounir B, Moalige B. CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES. New Trends in Mathematical Sciences. 2013;1:49–54.
MLA Kacha, Ali, et al. “CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES”. New Trends in Mathematical Sciences, vol. 1, no. 1, Apr. 2013, pp. 49-54, https://izlik.org/JA44AK87GN.
Vancouver 1.Ali Kacha, Brahim Ounir, Brahim Moalige. CONTINUED FRACTION EXPANSIONS OF SOME FUNCTIONS OF POSITIVE DEFINITE MATRICES. New Trends in Mathematical Sciences [Internet]. 2013 Apr. 1;1(1):49-54. Available from: https://izlik.org/JA44AK87GN