Math 482, Spring 2001.
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Adaptive Approximation
meets in 207-A Eckhart Hall
on Tuesdays and Thursdays from 1:30-2:50pm. 

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The course will discuss topics related to adaptive 
approximation and error estimation in various 
contexts, including

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   (1)	numerical approximation of solutions of 
	partial differential equations (PDEs) by 
	piecewise polynomials on adaptive meshes,

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   (2)	development and analysis of residual-based 
	error estimators for approximations of 
	solutions of PDEs and
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   (3)	nonlinear approximation in statistical 
	learning theory.

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One objective of the course will be to present these 
different areas in a context where objectives and 
techniques from one area can be used effectively in 
the other. Questions we hope to clarify are:

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    How can one develop error estimators to guide
    adaptation in computational learning theory?
    (I.e., how can the theory in 2 be applied to 3?)

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    How can techniques of learning theory be used to
    model decision processes governed by PDEs?
    (I.e., how can the theory in 3 be applied to 1?)

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The course will be self-contained, with the only
prerequisite being familiarity with real analysis.

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