Quantization as a consequence of the finite precision of words that represent the converted values.

In practice, finite precision is used and the result is an approximation of the true solution (assuming stability).

While in terms of functional analysis such problems are typically continuous, they may suffer from numerical instability when solved with finite precision, or with errors in the data.

Furthermore, there is evidence that Bruun's algorithm may be intrinsically less accurate than Cooley-Tukey in the face of finite numerical precision (Storn, 1993).

A process called renormalization keeps the finite precision from becoming a limit on the total number of symbols that can be encoded.

The problem here is that random floating-point numbers, however carefully generated, always have only finite precision.

The first is caused by the finite precision of computations involving floating-point or integer values.

For this reason, we refer to USM and bUSM implementations with finite precision coordinates as bounded scale independent representations.

He also developed the Kahan summation algorithm, an important algorithm for minimizing error introduced when adding a sequence of finite precision floating point numbers.

This is related to the finite precision with which computers generally represent numbers.