TY - GEN
T1 - Exact numerical computation in algebra and geometry
AU - Yap, Chee K.
PY - 2009
Y1 - 2009
N2 - Many problems in Computational Science & Engineering (CSE) are defined on the continuum. Standard algorithms for these problems are numerical and approximate. Their computational techniques include iteration, subdivision, and approximation. Such techniques are rarely seen in exact or algebraic algorithms. In this tutorial, we discuss a mode of computation called exact numerical computation (ENC) that achieves exactness through numerical approximation. Through ENC, we can naturally incorporate iteration, subdivision and approximation into the design of exact algorithms for computer algebra and computational geometry. Such algorithms are both novel and practical. This tutorial on ENC is divided into three equal parts: (a) Zero Problems (b) Explicitation Problems (c) Techniques and Complexity Analysis of Adaptivity.
AB - Many problems in Computational Science & Engineering (CSE) are defined on the continuum. Standard algorithms for these problems are numerical and approximate. Their computational techniques include iteration, subdivision, and approximation. Such techniques are rarely seen in exact or algebraic algorithms. In this tutorial, we discuss a mode of computation called exact numerical computation (ENC) that achieves exactness through numerical approximation. Through ENC, we can naturally incorporate iteration, subdivision and approximation into the design of exact algorithms for computer algebra and computational geometry. Such algorithms are both novel and practical. This tutorial on ENC is divided into three equal parts: (a) Zero Problems (b) Explicitation Problems (c) Techniques and Complexity Analysis of Adaptivity.
KW - Adaptive complexity analysis
KW - Exact numerical computation
KW - Explicitization problems
KW - Numerical algebraic computation
KW - Numerical computational geometry
KW - Zero bounds
UR - http://www.scopus.com/inward/record.url?scp=77950415436&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77950415436&partnerID=8YFLogxK
U2 - 10.1145/1576702.1576757
DO - 10.1145/1576702.1576757
M3 - Conference contribution
AN - SCOPUS:77950415436
SN - 9781605586090
T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
SP - 387
EP - 388
BT - ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
T2 - 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
Y2 - 28 July 2009 through 31 July 2009
ER -