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.

**[1]**Jan Ole Aasen,*On the reduction of a symmetric matrix to tridiagonal form*, Nordisk Tidskr. Informationsbehandling (BIT)**11**(1971), 233–242. MR**0288944****[2]**J. R. Bunch,*Analysis of the diagonal pivoting method*, SIAM J. Numer. Anal.**8**(1971), 656–680. MR**0292280**, https://doi.org/10.1137/0708061**[3]**James R. Bunch,*Partial pivoting strategies for symmetric matrices*, SIAM J. Numer. Anal.**11**(1974), 521–528. MR**0362856**, https://doi.org/10.1137/0711043**[4]**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**0428694**, https://doi.org/10.1090/S0025-5718-1977-0428694-0**[5]**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**, https://doi.org/10.1007/BF01399088**[6]**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**0305564**, https://doi.org/10.1137/0708060**[7]**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.**[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*, Oxford, at the Clarendon Press, 1955. MR**0074364****[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. 386-397.**[12]**R. C. Thompson,*Principal minors of complex symmetric and skew matrices*, Linear Algebra Appl.**28**(1979), 249–255. MR**549438**, https://doi.org/10.1016/0024-3795(79)90137-X**[13]**J. H. Wilkinson,*Error analysis of direct methods of matrix inversion*, J. Assoc. Comput. Mach.**8**(1961), 281–330. MR**0176602**, https://doi.org/10.1145/321075.321076**[14]**J. H. Wilkinson,*The algebraic eigenvalue problem*, Clarendon Press, Oxford, 1965. MR**0184422**

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Additional Information

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

Article copyright:
© Copyright 1982
American Mathematical Society