Abstract
The paper establishes explicit analytical representations of the errors and residuals of the solutions of linear algebraic systems as functions of the data errors and of the rounding errors of a high-accuracy floating-point arithmetic. On this basis, strict, componentwise, and in first order optimal error and residual estimates are obtained. The stability properties of the elimination methods of Doolittle, Crout, and Gauss are compared with each other. The results are applied to three numerical examples arising in difference approximations, boundary and finite element approximations of elliptic boundary value problems. In these examples, only a modest increase of the accuracy of the solutions is achieved by high-accuracy arithmetic.
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© 1986 Springer-Verlag Berlin Heidelberg
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Stummel, F. (1986). Strict optimal error and residual estimates for the solution of linear algebraic systems by elimination methods in high-accuracy arithmetic. In: Miranker, W.L., Toupin, R.A. (eds) Accurate Scientific Computations. Lecture Notes in Computer Science, vol 235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16798-6_7
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DOI: https://doi.org/10.1007/3-540-16798-6_7
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