least-squares technique

https://doi.org/10.1351/goldbook.L03492
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 y,x0,x1,... there are n measured values such as yi,x0i,x1i,... and it is decided to write a relation: y=f(a0,a1,...,aK;x0,x1,...) where a0,a1,...,aK are undetermined constants. If it is assumed that each measurement yi of y has associated with it a number wi1 characteristic of the uncertainty, then numerical estimates of the a0,a1,...,aK are found by constructing a
variable
S, defined by S=i(wi (yifi))2 and solving the equations obtained by writing Saj a˜j=0 a˜j=alla except aj. If the relations between the a and y are linear, this is the familiar least-squares technique of fitting an equation to a number of experimental points. If the relations between the a and y 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) on page 1822 [Terms] [Paper]