Reduction of functions of some partitioned matrices
Authors:
Victor LovassNagy and David L. Powers
Journal:
Math. Comp. 23 (1969), 127133
MSC:
Primary 65.35
MathSciNet review:
0238480
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Abstract: In the numerical analysis of physical problems, there often arise large matrices which exhibit certain kinds of blocksymmetry when partitioned appropriately. In this article, the structures of the frequentlyoccurring hypercirculant and hyperJacobi 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.
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 [1]
 S. Charmonman, ``An efficient algorithm for inverting a blocksymmetric matrix,'' Math. Comp., v. 21, 1967, pp. 715717.
 [2]
 E. Egerváry, ``On hypermatrices whose blocks are commutable in pairs and their applications in latticedynamics,'' Acta Sci. Math. Szeged, v. 15, 1954, pp. 211222. MR 16, 327. MR 0064736 (16:327d)
 [3]
 B. Friedman, ``Eigenvalues of compound matrices,'' Research Report TW16, 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. 712. 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. 95113. MR 0213048 (35:3913)
 [6]
 E. W. Montroll, ``Markoff chains and excluded volume effect in polymer chains,'' J. Chem. Phys., v. 18, 1950, pp. 734743. MR 12, 114. MR 0036468 (12:114e)
 [7]
 F. E. Steidler & H. H. Horovitz, ``The calculated loadcarrying ability of nonNewtonian lubricants in hydrodynamic bearings,'' Chemical Engineering Progress Symposium Series, no. 42, Vol. 59, 1963, pp. 99107.
 [8]
 J. Williamson, ``The latent root of a matrix of special type,'' Bull. Amer. Math. Soc., v. 37, 1931, pp. 585590. MR 1562202
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196902384808
PII:
S 00255718(1969)02384808
Article copyright:
© Copyright 1969 American Mathematical Society
