Midterm Specifications

  function  [X,rA,rB] = MatrixLS(A,B,C,delta)   
% A and B are m-by-n matrices (m>=n) and C is m-by-m.
% delta > 0.
% rA and rB are the delta-ranks of A and B.
% X is n-by-n, has at most rA*rB nonzero, and minimizes norm(A*X*B' - C,'fro') 
% assuming that A and B have ranks rA and rB, and 
 

  function x = BlockDD(D,E,F,k,b,j)
% D, E, and F are n-by-n matrices and k > 2 is a positive integer.
% Assume that M = A(D,E,F,k) is diagonally dominant so that it has a stable LU factorization.
% b is a column nk-by-1 vector and j is a positive integer.
% x is a column nk-by-1 vector that solves (M^j)x = b.

  function q = SingularToeplitz(r)
% Assume that r is a column n-1 vector and that the symmetric Toeplitz matrix
% T(r) is positive definite.
% q is a column n-1 vector with the property that if p = r(1:j) + q(j)*I(1:j,j), then 
% T(p) is singular
  
  function T = BorderLine(A)
% A is an n-by-n matrix with a safe LU factorization
% T is an n-by-(n-1) matrix with the property that for all i>=k,
% T(i,k) is the smallest tau (in absolute value)
% with the property that if A1 = A + tau*ei*ek'    (ei = I(:,i), ek = I(:,k))
% and C = A1(k:n,k:n) - A1(k:n,1:k-1)*inv(A1(1:k-1,1:k-1))*A1(1:k-1,k:n) then
% C(2:n-k+1,1)/C(1,1) has a component equal to one in absolute value.