Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Reduction of functions of some partitioned matrices

Authors: Victor Lovass-Nagy and David L. Powers
Journal: Math. Comp. 23 (1969), 127-133
MSC: Primary 65.35
MathSciNet review: 0238480
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the numerical analysis of physical problems, there often arise large matrices which exhibit certain kinds of block-symmetry when partitioned appropriately. In this article, the structures of the frequently-occurring hyper-circulant and hyper-Jacobi matrices are examined, and it is shown how the calculation of any analytic function of such matrices may be reduced to the calculation of functions of the submatrices. Examples drawn from current engineering literature are given as well as small illustrative examples.

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

  • [1] S. Charmonman, ``An efficient algorithm for inverting a block-symmetric matrix,'' Math. Comp., v. 21, 1967, pp. 715-717.
  • [2] E. Egerváry, ``On hypermatrices whose blocks are commutable in pairs and their applications in lattice-dynamics,'' Acta Sci. Math. Szeged, v. 15, 1954, pp. 211-222. MR 16, 327. MR 0064736 (16:327d)
  • [3] B. Friedman, ``Eigenvalues of compound matrices,'' Research Report TW-16, Mathematics Research Group, New York University Washington Square College of Arts and Science, 1951. MR 0042341 (13:95f)
  • [4] E. V. Haynsworth, ``Special types of partitioned matrices,'' J. Res. Nat. Bur. Standards Sect. B 65B, 1961, pp. 7-12. MR 27 #165. MR 0150162 (27:165)
  • [5] R. W. Hockney, ``A fast direct solution of Poisson's equation using Fourier analysis,'' J. Assoc. Comput. Mach., v. 12, 1965, pp. 95-113. MR 0213048 (35:3913)
  • [6] E. W. Montroll, ``Markoff chains and excluded volume effect in polymer chains,'' J. Chem. Phys., v. 18, 1950, pp. 734-743. MR 12, 114. MR 0036468 (12:114e)
  • [7] F. E. Steidler & H. H. Horovitz, ``The calculated load-carrying ability of non-Newtonian lubricants in hydro-dynamic bearings,'' Chemical Engineering Progress Symposium Series, no. 42, Vol. 59, 1963, pp. 99-107.
  • [8] J. Williamson, ``The latent root of a matrix of special type,'' Bull. Amer. Math. Soc., v. 37, 1931, pp. 585-590. MR 1562202

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.35

Retrieve articles in all journals with MSC: 65.35

Additional Information

Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society