TY - JOUR

T1 - Hypergeometric functions in Exact Geometric Computation

AU - Du, Zilin

AU - Eleftheriou, Maria

AU - Moreira, José E.

AU - Yap, Chee

N1 - Funding Information:
Supported by NSF/ITR Grant #CCR-0082056. Malaga, Spain (June 12-13, 2002).

PY - 2002/7

Y1 - 2002/7

N2 - Most problems in computational geometry are algebraic. A general approach to address nonrobustness in such problems is Exact Geometric Computation (EGC). There are now general libraries that support EGC for the general programmer (e.g., Core Library, LEDA Real). Many applications require non-algebraic functions as well. In this paper, we describe how to provide non-algebraic functions in the context of other EGC capabilities. We implemented a multiprecision hypergeometric series package which can be used to evaluate common elementary math functions to an arbitrary precision. This can be achieved relatively easily using the Core Library which supports a guaranteed precision level of accuracy. We address several issues of efficiency in such a hypergeometric package: automatic error analysis, argument reduction, preprocessing of hypergeometric parameters, and precomputed constants. Some preliminary experimental results are reported.

AB - Most problems in computational geometry are algebraic. A general approach to address nonrobustness in such problems is Exact Geometric Computation (EGC). There are now general libraries that support EGC for the general programmer (e.g., Core Library, LEDA Real). Many applications require non-algebraic functions as well. In this paper, we describe how to provide non-algebraic functions in the context of other EGC capabilities. We implemented a multiprecision hypergeometric series package which can be used to evaluate common elementary math functions to an arbitrary precision. This can be achieved relatively easily using the Core Library which supports a guaranteed precision level of accuracy. We address several issues of efficiency in such a hypergeometric package: automatic error analysis, argument reduction, preprocessing of hypergeometric parameters, and precomputed constants. Some preliminary experimental results are reported.

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U2 - 10.1016/S1571-0661(04)80378-5

DO - 10.1016/S1571-0661(04)80378-5

M3 - Conference article

AN - SCOPUS:18944367594

SN - 1571-0661

VL - 66

SP - 53

EP - 64

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

T2 - CCA 2002, Computability and Complexity in Analysis (ICALP 2002 Satellite Workshop)

Y2 - 12 July 2002 through 13 July 2002

ER -