% Lecture 3/18/02:
%  (1) Tridiagonal LU and solution
%     [l,u] = TriDiLU(d,e,f);
%  Tridiagonal LU without pivoting. d,e,f are n-vectors
%     y = LBiDiSol(l,b);
% Solves the nXn unit lower bidiagonal system   L*x = b
%     x = UBiDiSol(u,f,y);
% Solves the nXn upper bidiagonal system   U*x = b
%     ---- The SMW formula (hw3_1)
%  (2) Gaussian elimination without pivoting
%      [L,U] = GE(A);
% The LU factorization without pivoting. If A is nXn
% then L is unit low triangr and U is up triang so A = L*U.
%      y = LTriSol(L,b);
% Solves the nonsingular lower triangular system Lx = b.
%      x = UTriSol(U,y);
% Solves the nonsingular upper triangular system Ux = b.
% where U is nXn, b is nX1, and x is nX1 
% -----------------------
% Lecture 3/20/00
%  (1) Gauss elimination with pivoting
%    [L,U,piv] = GEpiv(A);      \
%    y = LTriSol(L,b(piv));     | same as x = A\b;
%    x = UTriSol(U,y);          /
%  (2) MATLAB routines
%    [L,U,P] = lu(A);   % can find piv as piv = P*(1:n)'
%    y = LTriSol(L,P*b);  % or y = L\P*b;
%    x = UTriSol(U,y);    % or x = U\y;  
%     ---- Partitioned problems (hw3_2)
%     ---- Linear combinations/ auxiliary conditions (hw3_3)