Arithmetic model

Numerical assay uses apparatus epsilon to abstraction the furnishings of rounding error. The complete errors of apparatus accession are far too complicated to be advised directly, so instead, the afterward simple archetypal is used. The IEEE accession accepted says all amphibian point operations are done as if it were accessible to accomplish the infinite-precision operation, and then, the aftereffect is angled to a amphibian point number. Suppose (1) , are amphibian point numbers, (2) is an accession operation on amphibian point numbers such as accession or multiplication, and (3) is the complete attention operation. According to the standard, the computer calculates:

By the acceptation of apparatus epsilon, the about absurdity of the rounding is at a lot of apparatus epsilon in magnitude, so:

where in complete consequence is at a lot of or u. The books by Demmel and Higham in the references can be consulted to see how this archetypal is acclimated to assay the errors of, say, Gaussian elimination.