A note on the stable decompostion of skew-symmetric matrices

Author:
James R. Bunch

Journal:
Math. Comp. **38** (1982), 475-479

MSC:
Primary 65F05

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645664-X

MathSciNet review:
645664

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Abstract | References | Similar Articles | Additional Information

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.

- Jan Ole Aasen,
*On the reduction of a symmetric matrix to tridiagonal form*, Nordisk Tidskr. Informationsbehandling (BIT)**11**(1971), 233–242. MR**288944**, DOI https://doi.org/10.1007/bf01931804 - J. R. Bunch,
*Analysis of the diagonal pivoting method*, SIAM J. Numer. Anal.**8**(1971), 656–680. MR**292280**, DOI https://doi.org/10.1137/0708061 - James R. Bunch,
*Partial pivoting strategies for symmetric matrices*, SIAM J. Numer. Anal.**11**(1974), 521–528. MR**362856**, DOI https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1137/0708060
F. Delale & F. Erdogan, "The effect of transverse shear in a cracked plate under skew-symmetric loading," - 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," - R. C. Thompson,
*Principal minors of complex symmetric and skew matrices*, Linear Algebra Appl.**28**(1979), 249–255. MR**549438**, DOI https://doi.org/10.1016/0024-3795%2879%2990137-X - J. H. Wilkinson,
*Error analysis of direct methods of matrix inversion*, J. Assoc. Comput. Mach.**8**(1961), 281–330. MR**176602**, DOI https://doi.org/10.1145/321075.321076 - J. H. Wilkinson,
*The algebraic eigenvalue problem*, Clarendon Press, Oxford, 1965. MR**0184422**

*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.

*BIT*, v. 10, 1970, pp. 386-397.

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Article copyright:
© Copyright 1982
American Mathematical Society