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- W2048568937 abstract "IN the solution of problems of linear algebra the majority of algebraic transformations reduce to calculating the scalar product of vectors, the product of a matrix by a vector, and the linear combination of vectors. This paper considers the distribution of founding errors when these operations are carried out on a computer with a fixed point, on the assumption that the original numbers are random variables. On fairly general assumptions about the initial value distribution a limiting error distribution is found for an infinite increase in the number of digits. An estimate of the deviation of the error distribution from the limiting distribution is given for the case where the distribution of the initial values satisfies some regularity conditions. The results are used to study the asymptotic behaviour of the errors on the solution of a system of linear algebraic equations by simple iteration methods." @default.
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- W2048568937 date "1969-01-01" @default.
- W2048568937 modified "2023-09-25" @default.
- W2048568937 title "Statistical study of the rounding errors of some algebraic transformations" @default.
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- W2048568937 doi "https://doi.org/10.1016/0041-5553(69)90075-5" @default.
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