Local surrogates
•
Modeling a wavy function with monomials is
inherently ill
‐
conditioned.
•
When we have a lot of data and we use
interpolation to predict function values in
between we normally use only values nearby.
•
For example, if we write down the price of
gasoline every first of the month from 2000
through 2009, how many values would you
use to estimate the price on June 15, 2007?

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Analogy to structural analysis
•
When we want to get the solution of structural
response with small number of equations, we use
Rayleigh
‐
Ritz procedure with global basis
functions.
•
When we can afford thousands of equations, we
use finite elements with local basis functions.
•
Local surrogates use basis functions that have
substantial values only over a small fraction of
design domain.