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Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View

Received: 27 March 2014     Accepted: 24 April 2014     Published: 10 May 2014
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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.

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

Keywords

Asymptotic Limits, Canonical Orthogonalization, Complex Zeros, Hermitian Metric Matrix, Positive-Definiteness, Symmetric Orthogonalization

References
[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.
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  • 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

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    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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    AMA 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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  • @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}
    }
    

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    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.
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Author Information
  • Department of Physics, Pondicherry University, Puducherry – 605014, India

  • School of Physics, University of Hyderabad, Hyderabad – 500 046, India

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