Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a property of numerical algorithms. It describes how errors in the input data propagate through the algorithm. In a stable method, the errors due to the approximations get damped out as the computation proceeds. In an unstable method, any errors in processing get magnified as the calculation proceeds. Unstable methods quickly generate garbage and are useless for numerical processing.

Related Topics:
Mathematical - Numerical analysis - Algorithm

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The numerical stability of a method together with the condition number defines how good a result one can get when using approximate methods to calculate a certain mathematical problem.

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Sometimes a single calculation can be achieved in several ways, all of which are algebraically identically in terms of ideal real or complex numbers, but in practice yield different results as they have different levels of numerical stability. One of the common tasks of numerical analysis is to try to select algorithms which are robust — that is to say, have good numerical stability in a wide range of situations.

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