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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Rounding Vectors?
Replies: 14   Last Post: Jul 2, 2012 12:04 AM

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Rounding Vectors?
Posted: Jun 26, 2012 12:07 PM
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Fix a positive integer N. Let V be the set of all x in R^N such that

x_1 + ... + x_N = 0.

Let W be the subset of points x in V such that each x_j is an integer.

What's a reasonable metric, such that there exists a simple algorithm
defining a function f : V -> W such that f(x) is one of the points of
W closest to x?

(It's a problem of great practical importance, heh-heh. I have these
backgammon scores. Each session defines an element of V. The game
is basically a dollar per point. In some sessions there were
beginners playing for dimes or quarters instead. I want to add up
all these sessions, but first I want to throw away the pennies
and round things to dollars. Except after the rounding the scores
for each session still have to add up to 0.)

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