function y = lu_find_y( y, a )
% See the Epage 163 in Wilmotts book: The Mathematics of Financial Derivatives
% 
% Written by:
% -- 
% John L. Weatherwax                2008-06-11
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

asq    = a*a; 
y(2)   = 1+2*a; 
%y(3:(end-1)) = 1+2*a - asq./y(2:(end-2));       % <- incorrect.  We cannot vectorize this in this way ... 
Nminus = 1; 
Nplus  = length(y); 
for n=3:(Nplus-1), 
  y(n) = 1+2*a - asq/y(n-1); 
  if( y(n)==0 ) error( 'failure / singular ...' ); end
end