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摘要
En 中文
The problem considered in this paper is that of consistently rounding off the elements of a matrix and its row and column sums. It is shown that a class of rounding problems of this kind is equivalent to a class of problems of determining flows through networks having arbitrary lower as well as upper bounds on edge flows. An existence theorem first proved by Hoffman for flows in such networks is used to show that an important subclass of the matrix rounding problems considered is always soluble. An algorithm for the entire class is illustrated by a numerical example.
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