Applied and Computational Mathematics
Volume 3, Issue 2, April 2014, Pages: 57-62
Received: Mar. 27, 2014;
Accepted: Apr. 24, 2014;
Published: May 10, 2014
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Ramesh Naidu Annavarapu, Department of Physics, Pondicherry University, Puducherry – 605014, India
Vipin Srivastava, School of Physics, University of Hyderabad, Hyderabad – 500 046, India
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.
Ramesh Naidu Annavarapu,
Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View, Applied and Computational Mathematics.
Vol. 3, No. 2,
2014, pp. 57-62.
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol.1, 3rd Ed., Interscience Publica-tion, NewYork (1953).
P-O. Löwdin; Ark. Mat. Astr. Fys. A. 35, (1947) pp. 9.
P.-O. Löwdin, Adv. Phys., 5, (1956), pp. 1.
V. Srivastava, J. Phys. A: Math. Gen. 33, (2000), pp. 6219-6222.
V. Srivastava, D. J. Parker, S. F. Edwards, J. Th. Biol. 253, (2008), pp. 514-517.
Ramesh Naidu and Vipin Srivastava, Int. J. Quan. Chem. 99(6), (2004), pp. 882-888.
Vipin Srivastava and A. Ramesh Naidu, Int. J. Quan. Chem. 106, (2006), pp. 1258-1266.
Horn and Johnson, Matrix Analysis, Cambridge University Press, (1989).
T. Jolliffe, Principal Component Analysis, Springer-Verlag, New York, (1986).
R. Rojas, Neural Networks, Springer, (1996).
Golub, H. Gene, Van Loan, F. Charles, Matrix Computations, 3rd Ed., The JohnHopkins University Press, (1996).
D. S. Watkins, Fundamentals of Matrix Computations, Wiley, NewYork, (1991), pp. 390-409.