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In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
This could include rounding errors, or errors introduced by the measuring device. When σ² η is known we can compute the reliability ratio as λ = ( σ² x − σ² η) / σ² x and reduce the problem to the previous case. Estimation methods that do not assume knowledge of some of the parameters of the model, include
Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem. [5] [6]
This type of rounding, which is also named rounding to a logarithmic scale, is a variant of rounding to a specified power. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale. For example, resistors are supplied with preferred numbers on a logarithmic scale.
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
Solving the unconstrained problem is equivalent to finding a point on the convex hull of the family of solutions to an equivalent constrained formulation of the problem. However, finding a solution – especially a closed-form solution – to any of these three problem formulations can be difficult.
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
The second, usually called Truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.