Tridiagonal systems 5、5fy d3 bbbbb e d, f3
Tridiagonal systems = 5 4 3 2 1 5 4 3 2 1 5 5 4 4 4 3 3 3 2 2 2 1 1 b b b b b x x x x x e d e d f e d f e d f d f = 5 4 4 3 3 2 2 1 1 5 4 3 2 5 5 4 4 4 3 3 3 2 2 2 1 1 1 1 1 1 1 u u f u f u f u f l l l l e d e d f e d f e d f d f
(i,-1):e1=l1→l1=e1/l1-1 (i,1):d1=,f1+l1→l1=d1-l,f n=length(d) zeros(n, 1) u=zeros u(1)=d(1); or 1=z'n u()=d()-l(i)*f(1-1) er
1 1 1 1 ( , ): ( , 1): / − − − − = + = − − = = i i i i i i i i i i i i i i i i d l f u u d l f i i e l u l e u n = length(d); l = zeros(n,1); u = zeros(n,1); u(1) = d(1); for i=2:n l(i) = e(i)/u(i-1); u(i) = d(i) - l(i)*f(i-1); end
function x=LBiDiSol(l, b) function x-UBiDiSol(u, f,b) n= length(b) n= length(b) x=zeros(n, 1) x=zeros(n, 1) x(1)=b(1) x(n)=b(n)/u(n) for i=2: n for i=n-1 x()=b()-l(1)*x(-1); x(1)=(b()-f(1)*x(i+1)/u(i) ei er Ly=b -
function x = LBiDiSol(l,b) n = length(b); x = zeros(n,1); x(1) = b(1); for i=2:n x(i) = b(i) - l(i)*x(i-1); end Ly=b function x = UBiDiSol(u,f,b) n = length(b); x = zeros(n,1); x(n) = b(n)/u(n); for i=n-1:-1:1 x(i) = (b(i) - f(i)*x(i+1))/u(i); end Ux=y