Other times these additional operations are worthwhile because they add numerical stability to the final result.

One problem with the Kalman filter is its numerical stability.

However, even this degree-two solution should be used with care to ensure numerical stability.

Note that minimum sampling requirements do not necessarily guarantee numerical stability.

In other contexts, for instance when solving differential equations, a different definition of numerical stability is used.

Numerical stability is an important notion in numerical analysis.

See the section Numerical stability in the following.)

Numerical stability can be a problem with this procedure and there are various ways of combating this instability.

The reduction in the number of arithmetic operations however comes at the price of a somewhat reduced numerical stability.

In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution.

The use of log probabilities improves numerical stability.

The method constitutes a significant improvement in distribution of nonlinearity and numerical stability over single shooting methods.

This method has greater numerical stability than the Gram-Schmidt method above.

This is a robust procedure that automatically selects a good set of redundant forces to ensure numerical stability.

As with other numerical situations, two main aspects are the complexity of algorithms and their numerical stability.

The new method provides increased numerical stability over traditional schemes at high Reynolds numbers (up to 9500) characteristic of turbulent flows.

Numerical stability is the central criterion for judging the usefulness of implementing an algorithm on a computer with roundoff.

This improves the numerical stability.

Subsequent developments, focussing on improving both efficiency and numerical stability, produced the following algorithms:

On the minus side, this scheme mandates an upper bound on the time-step to ensure numerical stability.

In numerical ordinary differential equations, various concepts of numerical stability exist, for instance A-stability.

Strassen's algorithm is more complex, and the numerical stability is reduced compared to naïve algorithm.

The usual definition of numerical stability uses a more general concept, called mixed stability, which combines the forward error and the backward error.

Such "partial pivoting" improves the numerical stability of the algorithm (see also pivot element); some variants are also in use.

Variants of this algorithm have been shown to be weakly stable (i.e. they exhibit numerical stability for well-conditioned linear systems).