I-Min Yang 



in which 



V 



V, 



~l -1 



V 2" V 1 



K + K - MCJ 

 o 



q cos 



q, cos 



Y6 



q l sm VI 



q 6 sin v 



(7) 



CO 



(8) 

 (9) 



and the superscript -1 for a matrix denotes its inverse. 



If the exact solution for the linear system is used as an 

 approximate solution for the nonlinear system, direct substitution 

 gives 



£ (z., k..) = f (x) - Ky + K z 

 1 ij o 



(10) 



where k^ are the (i, j) element of K and £ denotes the error vector. 

 The unknowns kj; are chosen in such a way that the average mean- 

 square error over one cycle defined by the integral 



i = 1 



d0, 



= ut 



(11) 



is a minimum. This leads to 



ae a 



dk 



ij 



o 



i, j = l 6 



12) 



676 



