Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extreme eigenvalues of Toeplitz forms and applications to elliptic difference equations


Author: Seymour V. Parter
Journal: Trans. Amer. Math. Soc. 99 (1961), 153-192
MSC: Primary 40.00; Secondary 42.00
MathSciNet review: 0120492
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] R. J. Arms, L. D. Gates and B. Zondek, A method of block iteration, J. Soc. Indust. Appl. Math. vol. 4 (1956) pp. 220-229. MR 0119405 (22:10167)
  • [2] S. D. Conte and R. T. Dames, An alternating direction scheme for the biharmonic difference equations, Math. Tables Aids Comput. vol. 12 (1958) pp. 198-205. MR 0105813 (21:4548)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. I. (English translation) New York, Interscience, 1953. MR 0065391 (16:426a)
  • [4] B. Friedman, The iterative solution of elliptic difference equations, A.E.C. Research and Development Report NYO--7698, New York University, 1957.
  • [5] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aids Comput. vol. 4 (1950) pp. 65-76. MR 0046149 (13:692e)
  • [6] U. Grenander and G. Szegö, Toeplitz forms and their applications, Berkeley, University of California Press, 1958. MR 0094840 (20:1349)
  • [7] J. Heller, Simultaneous, successive and alternating direction iteration schemes, J. Soc. Indust. Appl. Math. vol. 8 (1960) pp. 150-173. MR 0121978 (22:12705)
  • [8] F. B. Hildebrand, Introduction to numerical analysis, New York, McGraw-Hill, 1956. MR 0075670 (17:788d)
  • [9] E. Jahnke and F. Emde, Tables of functions with formulae and curves, New York, Dover Publications, 1943. MR 0008332 (4:281j)
  • [10] M. Kac, W. L. Murdoch, and G. Szegö, On the eigenvalues of certain Hermitian forms, J. Rational Mech. Anal. vol. 2 (1953) pp. 767-800. MR 0059482 (15:538b)
  • [11] H. Keller, On some iterative methods for solving elliptic difference equations, Quart. Appl. Math. vol. 16 (1958) pp. 209-226. MR 0117893 (22:8667)
  • [12] C. C. MacDuffee, The theory of matrices. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 2, Berlin, Springer, 1933.
  • [13] L. M. Milne-Thomson, The calculus of finite-differences, New York, Macmillan, 1933. MR 0043339 (13:245c)
  • [14] S. V. Parter, On ``two-line'' iterative methods for the Laplace and biharmonic difference equations, Numer. Math. vol. 1 (1959) pp. 240-252. MR 0128626 (23:B1664)
  • [15] R. D. Richtmyer, Difference methods for initial-value problems, New York, Interscience, 1958. MR 0093918 (20:438)
  • [16] D. E. Rutherford, Some continuant determinants arising in physics and chemistry. II, Proc. Roy. Soc. Edinburgh Sect. A. vol. 63 (1952) pp. 232-241. MR 0059232 (15:495d)
  • [17] Richard S. Varga, Iterative numerical analysis, Lecture Notes, Computation and Data Processing Center, University of Pittsburgh, 1959.
  • [18] -, Factorization and normalized iterative methods, Presented at the Symposium on Boundary Problems in Differential Equations at University of Wisconsin, April 1959, Westinghouse Report W.A.P.D.-T. 1950.
  • [19] H. Widom, On the eigenvalues of certain Hermitian operators, Trans. Amer. Math. Soc. vol. 88 (1958) pp. 491-522. MR 0098321 (20:4782)
  • [20] D. Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. vol. 76 (1954) pp. 92-111. MR 0059635 (15:562b)
  • [21] A. Zygmund, Trigonometrical series, New York, Dover, 1955. MR 0072976 (17:361e)
  • [22] G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Annals of Mathematics Studies, No. 27, Princeton University Press, 1951.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 40.00, 42.00

Retrieve articles in all journals with MSC: 40.00, 42.00


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1961-0120492-5
Article copyright: © Copyright 1961 American Mathematical Society