The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph.
| Published in | Applied and Computational Mathematics (Volume 3, Issue 2) |
| DOI | 10.11648/j.acm.20140302.13 |
| Page(s) | 57-62 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Asymptotic Limits, Canonical Orthogonalization, Complex Zeros, Hermitian Metric Matrix, Positive-Definiteness, Symmetric Orthogonalization
| [1] | R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol.1, 3rd Ed., Interscience Publica-tion, NewYork (1953). |
| [2] | P-O. Löwdin; Ark. Mat. Astr. Fys. A. 35, (1947) pp. 9. |
| [3] | P.-O. Löwdin, Adv. Phys., 5, (1956), pp. 1. |
| [4] | V. Srivastava, J. Phys. A: Math. Gen. 33, (2000), pp. 6219-6222. |
| [5] | V. Srivastava, D. J. Parker, S. F. Edwards, J. Th. Biol. 253, (2008), pp. 514-517. |
| [6] | Ramesh Naidu and Vipin Srivastava, Int. J. Quan. Chem. 99(6), (2004), pp. 882-888. |
| [7] | Vipin Srivastava and A. Ramesh Naidu, Int. J. Quan. Chem. 106, (2006), pp. 1258-1266. |
| [8] | Horn and Johnson, Matrix Analysis, Cambridge University Press, (1989). |
| [9] | T. Jolliffe, Principal Component Analysis, Springer-Verlag, New York, (1986). |
| [10] | R. Rojas, Neural Networks, Springer, (1996). |
| [11] | Golub, H. Gene, Van Loan, F. Charles, Matrix Computations, 3rd Ed., The JohnHopkins University Press, (1996). |
| [12] | D. S. Watkins, Fundamentals of Matrix Computations, Wiley, NewYork, (1991), pp. 390-409. |
APA Style
Ramesh Naidu Annavarapu, Vipin Srivastava. (2014). Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View. Applied and Computational Mathematics, 3(2), 57-62. https://doi.org/10.11648/j.acm.20140302.13
ACS Style
Ramesh Naidu Annavarapu; Vipin Srivastava. Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View. Appl. Comput. Math. 2014, 3(2), 57-62. doi: 10.11648/j.acm.20140302.13
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Download@article{10.11648/j.acm.20140302.13,
author = {Ramesh Naidu Annavarapu and Vipin Srivastava},
title = {Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View},
journal = {Applied and Computational Mathematics},
volume = {3},
number = {2},
pages = {57-62},
doi = {10.11648/j.acm.20140302.13},
url = {https://doi.org/10.11648/j.acm.20140302.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140302.13},
abstract = {The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph.},
year = {2014}
}
TY - JOUR T1 - Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View AU - Ramesh Naidu Annavarapu AU - Vipin Srivastava Y1 - 2014/05/10 PY - 2014 N1 - https://doi.org/10.11648/j.acm.20140302.13 DO - 10.11648/j.acm.20140302.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 57 EP - 62 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20140302.13 AB - The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph. VL - 3 IS - 2 ER -
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