A procedure for replacing the discrete set of results obtained from an experiment
by a continuous function. It is defined by the following.
For the set of variables
there are
measured values such as
and it is decided to write a relation:
where
are undetermined constants. If it is assumed that each measurement
of
has associated with it a number
characteristic of the uncertainty, then numerical estimates of the
are found by constructing a
variable, defined by
,
and solving the equations obtained by writing
except
.
If the relations between the
and
are linear, this is the familiar least-squares technique of fitting an equation to
a number of experimental points. If the relations between the
and
are non-linear, there is an increase in the difficulty of finding a solution, but
the problem is essentially unchanged.
Source:
PAC, 1981, 53, 1805
(Assignment and presentation of uncertainties of the numerical results of thermodynamic
measurements (Provisional))
on page 1822