A note on the stable decompostion of skew-symmetric matrices
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- by James R. Bunch PDF
- Math. Comp. 38 (1982), 475-479 Request permission
Abstract:
Computationally stable decompositions for skew-symmetric matrices, which take advantage of the skew-symmetry in order to halve the work and storage, are presented for solving linear systems of equations.References
- Jan Ole Aasen, On the reduction of a symmetric matrix to tridiagonal form, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 233–242. MR 288944, DOI 10.1007/bf01931804
- J. R. Bunch, Analysis of the diagonal pivoting method, SIAM J. Numer. Anal. 8 (1971), 656–680. MR 292280, DOI 10.1137/0708061
- James R. Bunch, Partial pivoting strategies for symmetric matrices, SIAM J. Numer. Anal. 11 (1974), 521–528. MR 362856, DOI 10.1137/0711043
- James R. Bunch and Linda Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Math. Comp. 31 (1977), no. 137, 163–179. MR 428694, DOI 10.1090/S0025-5718-1977-0428694-0
- James R. Bunch, Linda Kaufman, and Beresford N. Parlett, Hanbook Series Linear Algebra: Decomposition of a symmetric matrix, Numer. Math. 27 (1976), no. 1, 95–109. MR 1553989, DOI 10.1007/BF01399088
- J. R. Bunch and B. N. Parlett, Direct methods for solving symmetric indefinite systems of linear equations, SIAM J. Numer. Anal. 8 (1971), 639–655. MR 305564, DOI 10.1137/0708060 F. Delale & F. Erdogan, "The effect of transverse shear in a cracked plate under skew-symmetric loading," Trans. ASME, v. 46, 1979, pp. 618-624. J. J. Dongarra, J. R. Bunch, C. B. Moler & G. W. Stewart, LINPACK User’s Guide, SIAM, Philadelphia, Pa., 1979. 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.
- L. Mirsky, An introduction to linear algebra, Oxford, at the Clarendon Press, 1955. MR 0074364 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. 386-397.
- R. C. Thompson, Principal minors of complex symmetric and skew matrices, Linear Algebra Appl. 28 (1979), 249–255. MR 549438, DOI 10.1016/0024-3795(79)90137-X
- J. H. Wilkinson, Error analysis of direct methods of matrix inversion, J. Assoc. Comput. Mach. 8 (1961), 281–330. MR 176602, DOI 10.1145/321075.321076
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp. 38 (1982), 475-479
- MSC: Primary 65F05
- DOI: https://doi.org/10.1090/S0025-5718-1982-0645664-X
- MathSciNet review: 645664