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2. An estimate for the round-off error in the elimination problem

Author

B. A. Samokish and A. O. Rodnikov

Subjects
Statistics and Probability, Applied Mathematics, General Mathematics, System of linear equations, Conjugate gradient method, Linear form, Calculus, Bibliography, Applied mathematics, Round-off error, Coefficient matrix, Orthogonalization, Condition number, Mathematics
Abstract

The paper demonstrates that in computing a linear form (g, x) on the solution of a system of linear equations Ax = f, the round-off error depends on the quantities ‖A−1f‖ and ‖AT−1g‖ rather than on the condition number of the coefficient matrix A. Estimates of the inherent and round-off errors in solving the above problem by the orthogonalization method are provided. Numerical results confirming theoretical conclusions are presented. Bibliography: 8 titles.

Published
2007

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