A note on the stable decompostion of skewsymmetric matrices
Author:
James R. Bunch
Journal:
Math. Comp. 38 (1982), 475479
MSC:
Primary 65F05
MathSciNet review:
645664
Fulltext PDF Free Access
Abstract 
References 
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Abstract: Computationally stable decompositions for skewsymmetric matrices, which take advantage of the skewsymmetry in order to halve the work and storage, are presented for solving linear systems of equations.
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 [1]
 J. O. Aasen, "On the reduction of a symmetric matrix to tridiagonal form," BIT, v. 11, 1971, pp. 233242. MR 0288944 (44:6139)
 [2]
 J. R. Bunch, "Analysis of the diagonal pivoting method," SIAM J. Numer. Anal., v. 8, 1971, pp. 656680. MR 0292280 (45:1367)
 [3]
 J. R. Bunch, "Partial pivoting strategies for symmetric matrices," SIAM J. Numer. Anal., v. 11, 1974, pp. 521528. MR 0362856 (50:15294)
 [4]
 J. R. Bunch & L. Kaufman, "Some stable methods for calculating inertia and solving symmetric linear systems," Math. Comp., v. 31, 1977, pp. 163179. MR 0428694 (55:1714)
 [5]
 J. R. Bunch, L. Kaufman & B. N. Parlett, "Decomposition of a symmetric matrix," Numer. Math., v. 21, 1976, pp. 95109. MR 1553989
 [6]
 J. R. Bunch & B. N. Parlett, "Direct methods for solving symmetric indefinite systems of linear equations," SIAM J. Numer. Anal., v. 8, 1971, pp. 639655. MR 0305564 (46:4694)
 [7]
 F. Delale & F. Erdogan, "The effect of transverse shear in a cracked plate under skewsymmetric loading," Trans. ASME, v. 46, 1979, pp. 618624.
 [8]
 J. J. Dongarra, J. R. Bunch, C. B. Moler & G. W. Stewart, LINPACK User's Guide, SIAM, Philadelphia, Pa., 1979.
 [9]
 W. Graeff, W. Bauspiess, U. Bonse, M. Schlenker & H. Rauch, "Phase imaging with a skew symmetric LLL neutron interferometer," Acta Cryst. Sect. A, v. 34, 1978, p. 239.
 [10]
 L. Mirsky, An Introduction to Linear Algebra, Clarendon Press, Oxford, 1955. MR 0074364 (17:573a)
 [11]
 B. N. Parlett & J. K. Reid, "On the solution of a system of linear equations whose matrix is symmetric but not definite," BIT, v. 10, 1970, pp. 386397.
 [12]
 R. C. Thompson, "Principal minors of complex symmetric and skewmatrices," Linear Algebra Appl., v. 28, 1979, pp. 249255. MR 549438 (80j:15007)
 [13]
 J. H. Wilkinson, "Error analysis of direct methods of matrix inversion," J. ACM, v. 8, 1961, pp. 281330. MR 0176602 (31:874)
 [14]
 J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 0184422 (32:1894)
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DOI:
http://dx.doi.org/10.1090/S0025571819820645664X
PII:
S 00255718(1982)0645664X
Article copyright:
© Copyright 1982
American Mathematical Society
