A Study on the Behavior of Absolute Permanent Matrix Transformation

Suresh Kumar Sahani; Vishnu Narayan Mishra

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P517

A Study on the Behavior of Absolute Permanent Matrix Transformation

Suresh Kumar Sahani, Vishnu Narayan Mishra

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.

Keywords

Matrix method for summability, matrix transformation etc.

References

[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.

Citation :

Suresh Kumar Sahani, Vishnu Narayan Mishra, "A Study on the Behavior of Absolute Permanent Matrix Transformation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 122-127, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P517