How to Efficiently Approximate a Function of One or More Variables | by Ryan Burn | Jun, 2024

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Use sparse grids and Chebyshev interpolants to build accurate approximations to multivariable functions.

An adaptive sparse grid at Chebyshev-Gauss-Lobatto nodes. Figure by author.

Consider this approximation problem: Suppose you have a function f(x), x ∈ [-1, 1]^p, that is expensive to evaluate; and hence, you’d like to build a new function f’ that is…

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