Modified moments and gaussian quadratures

Rocky Mountain Journal of Mathematics

Volumn 4, Issue 2, 1974, Pages 287-296

  Wheeler, John C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000955005     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/RMJ-1974-4-2-287     Document Type: Article

References (24)

1. W. Gautschi, On the construction of Gaussian quadrature rules from modified moments, Math. Comp. 24 (1970), 245-260.
2. G. H. Golub, Some modified eigenvalue problems, paper presented at the Dundee Conference on Numerical Analysis at Dundee, Scotland, March, 1971.
3. G. H. Golub, Bounds for matrix moments, paper presented at the International Conference on Pade Approximants, Continued Fractions and Related Topics at Boulder, Colorado, June, 1972.
4. R. G. Gordon, Error bounds in equilibrium statistical mechanics, J. Math. Phys. 9 (1968), 655-663.
5. R. G. Gordon, Error bounds in spectroscopy and nonequilibrium statistical mechanics, J. Math. Phys. 9 (1968), 1087-1092.
6. W. B. Gragg, The continued fraction algorithm, Paper given at the International Conference on Pade Approximants, Continued Fractions and Related Topics, Boulder, Colorado, June 1972.
7. C. Isenberg, Moment calculations in lattice dynamics. I. fee lattice with nearest-neighbor interactions, Phys. Rev. 132 (1963), 2427-2433.
8. C. Isenberg, A method for extending the calculation of the number of even moments of the vibration frequency spectrum of a crystal, Journal of Physics C3, L179-L181.
9. C. Isenberg, Moment calculations in lattice dynamics II, Journal of Physics C4, 164-173.
10. Maradudin, Montroll, Weiss, Ipatova, Theory of Lattice Dynamics in Harmonic Approximation (2nd Ed.) Academic Press, 1971, 319 pages.
11. E. W. Montroll, Theory of vibration of simple cubic lattices with nearest- neighbor interactions, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California 3 (1956), 209-246.
12. J. C. Phillips, Critical points and lattice vibration spectra, Phys. Rev. 104 (1956), 1263-1277.
13. H. B. Rosenstock, Dynamics of simple lattices, Phys. Rev. 97 (1955), 290-303.
14. H. Rutishauser, Der Quotienten-Differ enze-Algorithmus, Birkhauser, Basel/Stuttgart, 1947
15. H. Rutishauser, Der Quotienten-Differ enze-Algorithmus, Birkhauser, Basel/Stuttgart, P. Henrici Proc. Symp. Appl. Math. 15 (1963), 159.
16. R. A. Sack and A. F. Donovan, An algorithm for Gaussian quadrature given modified moments, Numer. Math. 18 (1972), 465-478.
17. Z. W. Salsburg and D. A. Huckaby, Free energy of the fee and hep lattices under first- and second-neighbor harmonic interactions, J. Comp. Physics 7 (1971), 489-501.
18. L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89 (1953), 1189-1193.
19. H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand, 1948, Chapter 11, pp. 196-199.
20. J. C. Wheeler and C. Blumstein, Modified-moments method: applications to harmonic solids, Phys. Rev. B 8 (1973), 1764-1776.
21. J. C. Wheeler and R. G. Gordon, Rigorous bounds for thermodynamic properties of harmonic solids, J. Chem. Phys. 51 (1969), 5566-5583.
22. J. C. Wheeler, Rigorous bounds from moment constraints, in The Pade Approxi-mant in Theoretical Physics, Edited by G. A. Baker, Jr. and J. L. Gammell, New York, Academic Press, 1970, Chapter 3.
23. J. C. Wheeler and C. Blumstein, Modified moments for harmonic solids, Phys. Rev. B 6 (1972), 4380-4382.
24. J. C. Wheeler and Robert I. Cukier, to be published.