>^ - f(Xj, a^ + Aa, b^ + Ab) - y^^ , 1 - l,2,...,n 



V + yl » f(x , a + Aa, b + Ab),l - 1.2,. ..,n 



Expanding the right side by Taylor's Theorem for the two variables, 

 a and b, yields 



3f 3f 

 v^ +y^ - f(xj^, a^, b^) + Aa(^) + Ab(g^) + ...; 1 - l,2,...,n 



o o 



substituting y'j " f(x^» a , b ) we have 



3f 3f 

 v^ + y^ - y'i + Ab(^) + Ab(^) + ...; 1 - l,2,...,n 

 o o 



Rearranging terms and dropping higher order derivatives yields 



3f 3f 



"l " ^^^^^ "^ ^^^TT"^ * y'l " ^1*' ^ " ^'2 n. 



o o 



Ue define 



'l " y'l " ^1 ^ " l»2."«»a 



where the r's are the residuals £or the approximation curve 



y' ■ f(x ,a ,b ). Substituting, we can write our residual equations 

 o o 



128 



