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Equation 1 · Part 3 · Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation

Symbol f

f^(x)=f(x)+εdisc(h)+εround(u)+εmodel\hat{f}(x) = f(x) + \varepsilon_{\text{disc}}(h) + \varepsilon_{\text{round}}(u) + \varepsilon_{\text{model}}
ff

What this part means

f is part of the quantity the equation computes from the expression on the right.

Its job in the formula

f is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…different kind of project than “run the simulation twice as long.” f^(x)=f(x)+εdisc(h)+εround(u)+εmodel\hat{f}(x) = f(x) + \varepsilon_{\text{disc}}(h) + \varepsilon_{\text{round}}(u) + \varepsilon_{\text{model}}. This decomposition is worth writing out because it names what a reported simulation number actually is: not the true answer f(x) , but a sum of the true answer with a discretization error that shrinks with step size h , a rounding error governed by machine precision u , and — the term simulations share with no other approach on this list — an irreducible modeling error from every simplifying assumption baked into the…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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