A Study on the Behavior of Absolute Permanent Matrix Transformation

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Suresh Kumar Sahani, Vishnu Narayan Mishra
  10.14445/22315373/IJMTT-V66I12P517

MLA

MLA Style: Suresh Kumar Sahani, Vishnu Narayan Mishra  "A Study on the Behavior of Absolute Permanent Matrix Transformation" International Journal of Mathematics Trends and Technology 66.12 (2020):122-127. 

APA Style: Suresh Kumar Sahani, Vishnu Narayan Mishra(2020). A Study on the Behavior of Absolute Permanent Matrix Transformation.  International Journal of Mathematics Trends and Technology, 122-127.

Abstract
The study of infinite matrices is important in the theory of summability and in approximation. In this paper, we propose to use a more general matrix method to obtain the necessary and sufficient conditions to the absolute permanent matrix transformation.

Reference

[1] Bojanczyk, A. W,. Brent R. P,. Hong F. R. and Sweet. D. R., "On the stability of the Burier and related Toepliz factorization algorithm", SIAM journal on Matrix Analysis and Applications, 16: 40-57, (1995).
[2] Boss, L. and Levenberg, N. and Waldron, S., Matrices associated to multivariate polynomials inequalities. In advance in constructive Approximations, M. Neamtu and E.B. Saffeds, Nashboro press, Nashville, 133-147, (2004).
[3] Obrechkoff, N, Formules asymptotiques pour les polynόmes de Jacobi et sur les series suivant les memes polynόmes, Ann.Univ.32,39-135, (1936).
[4] Wilson and Bidwell E., A history of the theories from the age Descartes to the close of the nineteenth century, Bulletin of the American Mathematical Society,26(4),183-184, (1913).
[5] Sunouchi, On the Riemann summability, Tehoku M. J., (2), 5 (1983)
[6] Mohiuddin S.A, Matrix transformation of performed sequence spaces through dela Vallie- Pousin mean, Acta Scientiarum Technology. 37(1):71-75, (2015).
[7] Mursaleen MD. And Mohiddine S.A, Almost bounded variation of double sequences and some four-dimensional summability matrices, Publ. Math. Debrecen75 |3-4|, 495-508, (2009).
[8] Böttcher, Albrecht, Grudsky, Sergei, M., Toeplitz matrices, Asymptotic Linear Algebra, and Functional analysis, Birkhauser, ISBN 978-3-0348-8395-5, (2012).
[9] Brent, R.P., Stability of fast algorithms for structured linear system in Kailth, T, Sayed, A. H.(eds), Fast Reliable Algorithms for Matrices with Structure, SIAM,103-116, (1999)
[10] Yang, ZaiXie, Lihua, Stoica, Petre, Vandermonde decomposition in multilevel Toeplitz matrices with application on to multidimensional Super-resolution, IEEE Transactions on Information theory,62(6),3685-3701, (2016)
[11] Ye, Ke, Lim, Lek-Heng, every matrix is a product of Toeplitz matrices, Foundation of Computational Mathe-matics,16(3),577-598, (2016).
[12] Rogosinski, W. W., Obituary. Michael Fekete, Journal of the London Mathematical Society, Second Ser-ies,33,496-500, (1958).
[13] Toe plitz, O, U  ber allgemeine lineare Mittelbildungen, Prace Mat. Fiz, 22, 113-119,(1911).
[14] Lorentz, G.G. A contribution to the theory of divergent series. Acta Mathematica, 80, 167-190 (1998).
[15] Mazhar, S.M. and A.H. Siddiqui, on almost summability of trigonometrical sequence, Acta Mathematica Acad. Science, Hung. (1-2), 20, 21-24 (1969).
[16] King, JP: Almost Summable sequences. proc. Am. math. Soc. 17, 1219-1258 (1966).
[17] Zygmund, A., Trigonometric series, Cambridge university press, London (1959).
[18] Mittal, ML and Mishra, VN, Int. J. of Math. Sci. and Engg. Appls 2, 1-9, 2008.
[19] Mishra LN, Mishra VN, Khatri Kejal and Deepmala, Applied Mathematics and Computation, vol. 237, 252-263, 15 June 2014.

Keywords : Matrix method for summability, matrix transformation etc.