Numerical Stability - Error Growth

Error Growth

Suppose that Ei > 0 denotes an initial error and En represents the magnitude of an error after n subsequent operations. If En ∼  C∙n∙Ei, where C is a constant independent of n, then the growth of the error is said to be linear. If En ∼  Cn∙Ei, for some C > 1, then the growth of the error is called exponential.

Read more about this topic:  Numerical Stability

Famous quotes containing the words error and/or growth:

    “Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus “theoretically,” is to use language in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.”
    —Charles Sanders Peirce (1839–1914)

    “When I have plucked the rose,
    I cannot give it vital growth again,
    It needs must wither. I’ll smell it on the tree.”
    —William Shakespeare (1564–1616)