TY - GEN

T1 - In Praise of numerical computation

AU - Yap, Chee K.

PY - 2009

Y1 - 2009

N2 - Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms' design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name "numerical computational geometry" for suchf activities.

AB - Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms' design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name "numerical computational geometry" for suchf activities.

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U2 - 10.1007/978-3-642-03456-5_26

DO - 10.1007/978-3-642-03456-5_26

M3 - Conference contribution

AN - SCOPUS:70349854898

SN - 3642034551

SN - 9783642034558

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 380

EP - 407

BT - Efficient Algorithms

A2 - Albers, Susanne

A2 - Alt, Helmut

A2 - Naher, Stefan

ER -