

*(2/3 A(y^^j- ydelj) 



-1/3 



+ A AX A (y, - ydel, ) 

 (D-7-2) 



2/3 



dF dg "^^^^ r 



meas 



IMAX.j 



A(y 



IMAX.j 



.-ydel 



IMAX 



2/3 

 ) ) 



*(2/3 A(yj^^xj-yd^hMAx)"^''^^ ^ X AX A (y^ - ydel,^^)^^^ 



(D-7-(IMAX+l)) 



meas 



IMAX 



S 



1 = 1 



5/3, 



(3/5 AX A(y^- ydelj)"'") 



(D-7-(IMAX+2)) 



Because Equations (D-7) is a system of nonlinear equations, it can not 

 be written in matrix form as a [D] [x] = [E] system of equations (the 

 brackets denote matrices). To solve the equations, a Newton-Raphson Iteration 

 technique for nonlinear equations was used. This is done by differentiating 

 each of the (IMAX + 2) equations with respect to each of the unknowns, the 

 resulting equations are then linear in terms of Aa, Aydeli, . . . 

 Aydel IMAX ax . The resulting matrix is inverted to obtain the A(unknown) 

 and the quantities are added to the original estimates to produce a better 

 estimate. This iterative procedure is continued until the changes become 

 acceptably small. The solution converged rapidly. Generally, the first row 

 of the matrix to be inverted is (an represents the kl!l row and the IJ^l 

 column of the matrix). 



IMAX JMAX 



a,, = Z Z 2(y 



i=l j=l 



'11 



i.j -y''h^ 



4/3 



JMAX 



^1,2 " ^ 



j = l 



^^l.j ■^^^h^"'''(Vas.^. -2^(^l.j-^^^h)'^') 



104 



