Symbol kappa
kappa is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
Numerical analysis has always run on an analogous verification principle, just usually informal: an error bound is only useful if it is derived from and checkable against a stated model of arithmetic. The classical example is the sensitivity of a linear system to input error, captured by the condition number of a matrix A : . If is large, small errors in the input data or in floating-point rounding can produce large errors in the computed solution, independent of which algorithm is used to solve the system — a property of the problem, not the solver. Bringing formal verification to numerical software means proving that an implementation’s actual rounding behavior…
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Symbol A
A is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol A^-1
1 is one of the signed contributions combined to compute the quantity on the left.
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Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 6 · Mathematics
Mathematics, Proof, and Scientific Computation in 2035: Scenarios, Signals, and Falsifiable Predictions
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Numerical analysis has always run on an analogous verification principle, just usually informal: an error bound is only useful if it is derived from and checkable against a stated model of arithmetic. The classical example is the sensitivity of a linear system to input error, captured by the condition number of a matrix A : . If is large, small errors in the input data or in floating-point rounding can produce large errors in the computed solution, independent of which algorithm is used to solve the system — a property of the problem, not the solver. Bringing formal verification to numerical software means proving that an implementation’s actual rounding behavior…
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