On factoring a class of complex symmetric matrices without pivoting

Author:
Steven M. Serbin

Journal:
Math. Comp. **35** (1980), 1231-1234

MSC:
Primary 65F05

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583500-9

MathSciNet review:
583500

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Abstract: Let be a complex, symmetric matrix with and each real, symmetric and positive definite. We show that the LINPACK diagonal pivoting decomposition proceeds without the necessity for pivoting. In particular, when and are band matrices, bandwidth is preserved.

**[1]**J. R. BUNCH & L. KAUFMAN, "Some stable methods for calculating inertia and solving symmetric linear systems,"*Math Comp.*, v. 31, 1977, pp. 163-179. MR**0428694 (55:1714)****[2]**J. R. BUNCH, L. KAUFMAN & B. N. PARLETT, "Decomposition of a symmetric matrix,"*Numer. Math.*, v. 27, 1976, pp. 95-109. MR**1553989****[3]**J. J. DONGARRA, C. B. MOLER, J. R. BUNCH & G. W. STEWART,*LINPACK User's Guide*, SIAM, Philadelphia, Pa., 1979.**[4]**G. FAIRWEATHER, "A note on the efficient implementation of certain Padé methods for linear parabolic problems,"*BIT*, v. 18, 1978, pp. 106-109. MR**0488820 (58:8326)****[5]**B. WENDROFF,*Theoretical Numerical Analysis*, Academic Press, New York, 1966. MR**0196896 (33:5080)**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583500-9

Article copyright:
© Copyright 1980
American Mathematical Society