On the complexity of familiar functions and numbers

Title: On the complexity of familiar functions and numbers
Creator: Borwein, J. M.; Borwein, P. B.
Relation: SIAM review Vol. 30, Issue 4, p. 589-601
Publisher Link: http://dx.doi.org/10.1137/1030134
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Resource Type: journal article
Date: 1988
Description: This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious. For most functions, provably optimal methods are not known; however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.
Subject: elementary functions; pi; low-complexity approximation; reduced-complexity approximation; rational approximation; algebraic approximation; computation of digits; open problems
Identifier: http://hdl.handle.net/1959.13/940748
Identifier: uon:13093
Identifier: ISSN:0036-1445
Language: eng
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