NDLI: “Simple” approximations

Content Provider	ACM Digital Library
Author	Schwartz, Benjamin L.
Abstract	For the purpose of this paper, we shall define a “simple” approximation to the real number X, X > O, as a number of the form (1) (equation) where A, B, C, and D are positive integers less than some preassigned upper limit M, and such that (2) (equation) for some preassigned t > O. We shall generally be concerned with the set of all approximations of this form; this set we shall call the simple approximation set (SAS). We shall call M the simplicity modulus of the SAS, and t the approximation modulus. For any simplicity modulus M, there are M4 possible fractions of form (1), which must be tested against condition (2) to determine whether they are in the SAS. In practice, this number can be greatly reduced. Symmetry and nonuniqueness of factorization enable more than three-quarters of them to be discarded. A further reduction often follows from another argument: For any A, B, and D, the best estimate of C is [equation].
Starting Page	29
Ending Page	32
Page Count	4
File Format	PDF
DOI	10.1145/800258.808941
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1956-01-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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“Simple” approximations