Symbol hatf
hatf is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
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 argument both aim at f(x) exactly; a simulation reports and, if it is honest, reports an estimate of how large the three error terms might be.
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Symbol x
x is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Read this expression with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 6 · Mathematics
Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
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 argument both aim at f(x) exactly; a simulation reports and, if it is honest, reports an estimate of how large the three error terms might be.
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