Table rounding problem
Jiřı́ Šı́ma · 1999
From time to time, people dealing with accounting are faced with the following table rounding problem. Consider a m \\Theta n table with numerical values (e. g., amount of money) in which the last column contains check sums of numbers in particular rows. Similarly, the last row consists of column check sums. A new table is to be produced in which the original numbers, and check sums are rounded off (e. g., to integers). However, the classical rounding procedure (i. e., rounding fractions smaller than 0.5 down, otherwise up) can generally violate the validity of sums. Therefore, the possibility to round off the non-integer numbers in the table to adjacent integers (i. e., either up or down independently on their fractions) is explored in order to preserve the check sums. We formulate a necessary and sufficient condition stating when rounding, which is consistent with prescribed (integer) check sums, exists. We also prove that such rounding always exists providing that the rounding of c...