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Equation 1 · Part 5 · Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation

Symbol h

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}}
hh

What this part means

h is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

h is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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 equations themselves before any computer touches them. A formal proof and a peer-reviewed…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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