Chapter 16, Problem 16.1P

To determine

Fundamental conditions enforced by weighted least-squares.

Explanation of Solution

The fundamental condition enforced by weighted least-squares is that the sum of the sum of the squares of the residual is a minimum. For example, a group of n equally weighted measurements were taken having residuals $v_1$ , $v_2$ ,….., $v_n$ then the fundamental condition of the weighted least-squares is expressed in equation form as follows.

  ${\displaystyle \sum _{i=1}^n{v}_i^2=v_1^2+v_2^2+\mathrm{....}+v_n^2}=\text{minimum}$