Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method

摘要

From the point of view that no mathematical method can ever minimize or alter errors already made in a physical measurement, the classical least squares method has severe limitations which make it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimized, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one.