Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

The infinity norm of a certain type of symmetric circulant matrix


Authors: W. D. Hoskins and D. S. Meek
Journal: Math. Comp. 31 (1977), 733-737
MSC: Primary 65F35
DOI: https://doi.org/10.1090/S0025-5718-1977-0433849-5
MathSciNet review: 0433849
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An attainable bound for the infinity norm of the inverse of a whole class of symmetric circulant Toeplitz matrices is found. The class of matrices includes those arising from interpolation with both odd and even degree periodic polynomial splines on a uniform mesh.


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

  • [1] M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, Dover, New York, 1966. MR 34 #8606. MR 0208797 (34:8606)
  • [2] J. H. AHLBERG, E. N. NILSON & J. L. WALSH, The Theory of Splines and Their Applications, Academic Press, New York and London, 1967. MR 39 #684. MR 0239327 (39:684)
  • [3] E. L. ALBASINY & W. D. HOSKINS, "Explicit error bounds for periodic splines of odd order on a uniform mesh," J. Inst. Math. Appl., v. 12, 1973, pp. 303-318. MR 49 #6546. MR 0341800 (49:6546)
  • [4] W. D. HOSKINS, "Some properties of a certain class of circulant matrices," Proc. Manitoba Conf. on Numerical Mathematics, Univ. of Manitoba, Winnipeg, Canada, 1971, pp. 361-372. MR 49 #938. MR 0336162 (49:938)
  • [5] W. D. HOSKINS & D. S. MEEK, "Linear dependence relations for polynomial splines at midknots," BIT, v. 15, 1975, pp. 272-276. MR 52 #12291. MR 0391470 (52:12291)
  • [6] D. S. MEEK, On the Numerical Construction and Approximation of Some Piecewise Polynomial Functions, Ph.D. thesis, Univ. of Manitoba, Canada, 1973.
  • [7] T. MUIR, A Treatise on the Theory of Determinants, rev. ed., Dover, New York, 1960. MR 22 #5644. MR 0114826 (22:5644)
  • [8] R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)
  • [9] R. S. VARGA, W. J. KAMMERER & G. W. REDDIEN, "Quadratic interpolatory splines," Numer. Math., v. 22, 1974, pp. 241-259. MR 52 #2132. MR 0381235 (52:2132)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F35

Retrieve articles in all journals with MSC: 65F35


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0433849-5
Keywords: Infinity norm of circulant matrix, periodic polynomial splines
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society