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主讲人： Lloyd Nick Trefethen教授
英国牛津大学
报告题目：CHEBFUN: A NEW KIND OF NUMERICAL COMPUTING
报告时间：2011年11月11日15：00
报告地点：海韵园教学楼504报告厅
报告摘要：
For a long time there have been two kinds of
mathematical computation: symbolic and numerical. Symbolic
computing manipulates algebraic expressions exactly, but it is
unworkable for many applications since the space and time
requirements tend to grow combinatorially. Numerical computing
avoids the combinatorial explosion by rounding to 16 digits at each
step, but it works just with individual numbers, not algebraic
expressions.
This talk will describe a new kind of computing that aims to combine the feel of symbolics with the speed of numerics. The idea is to represent functions by Chebyshev expansions whose length is determined adaptively to maintain an accuracy of close to machine precision. Our Chebfun system is implemented in object-oriented Matlab, with familiar vector operations such as sum and diff overloaded to analogues for functions such as integration and differentiation. Building on this foundation, we have even overloaded "backslash" to solve linear and nonlinear differential equations. Chebfun is joint work with many people including Toby Driscoll and Nick Hale: see www.maths.ox.ac.uk/chebfun/.
报告人简介：
Lloyd N.Trefethen是英国牛津大学教授, 世界顶尖的数值分析专家，
美国国家工程院院士，英国皇家学会院士,
和现任SIAM（国际工业与应用数学学会）主席。曾获MIT教学奖、康奈尔大学教学奖、牛津大学教学奖、欧洲研究理事会基金（European
Research Council Advanced Grant）、IMA金奖，并因其在数值分析领域杰出的成就获第一届Leslie
Fox奖。