Algorithm for numerical method

Pagina 1

Calcolo Numerico 1 Algoritmi per Metodi Numerici Massimo Piazza fwsub.m y1 = b1 l11 for i =2: n yi = 1 lii ( bi− i−1∑ j=1 lijyj ) end y = zeros (n ,1) ; y (1) = b (1) / L (1 ,1) ; for i =2: n y ( i ) =( b ( i ) -L (i ,1: i -1) * y (1: i -1) ) / L (i , i ) ; end bksub.m xn = yn unn for i =n -1:1 xi = 1 uii ( yi− n∑ j=i+1 uijxj ) end x = zeros (n ,1) ; x ( n ) = b ( n ) / U (n , n ) ; for i =n -1: -1:1 x ( i ) =( b ( i ) -U (i , i +1: n ) * x ( i +1: n ) ) / U (i , i ) ; end lugauss.m A (1) =A for k =1: n -1 for i = k +1: n lik = a(k) ik a(k) kk for j = k +1: n a(k+1) ij =a(k) ij −lika(k) kj end end end n = length ( diag ( A ) ) ; L = eye ( n ) ; for k = 1: n -1 for i = k +1: n l_ik = A (i , k ) / A (k , k ) ; L (i , k ) = l_ik ; if l_ik == 0 error ( ’ Pivot nullo ’) end for j = k +1: n A (i , j ) = A (i , j ) - l_ik * A (k , j ) ; end end end U = triu ( A ) ; L = tril ( L ) ; 2 thomas.m (being A =LU ) α1 =a1 for i =2: n βi−1 = ei−1 αi−1 αi =ai−βi−1ci−1 end (solve Ly = b) for i =2: n y1 =b1 yi =bi−βi−1yi−1 end (solve U x = y) for i =n -1:1 xn = yn αn xi = yi−cixi+1 αi end n = length ( diag ( A ) ) ; c = diag (A , 1) ; a = diag ( A ) ; e = diag (A , -1) ; alpha = zeros (n ,1) ; bet = zeros (n -1 ,1) ; alpha (1) = a (1) ; for i = 2: n bet (i -1) = e (i -1) / alpha (i -1) ; alpha ( i ) = a ( i ) - bet (i -1) * c (i -1) ; end y = zeros (n -1 ,1) ; y (1) = b (1) ; for i = 2: n y ( i ) = b ( i ) - bet (i -1) * y (i -1) ; end x = zeros (n -1 ,1) ; x ( n ) = y ( n ) / alpha ( n ) ; for i = n -1: -1:1 x ( i ) = ( y ( i ) - c ( i ) * x ( i +1) ) / alpha ( i ) ; end L = eye ( n ) + diag ( bet , -1) ; U = diag ( alpha ,0) + diag (c ,1) ; 3 jacobi.m choose x(0) r(0) = b−Ax(0) for k =0 ,1 ,... solve Dz(k) = r(k) x(k+1) = x(k) + z(k) r(k+1) = b−Ax(k+1) end if ( prod ( diag ( A ) ) ==…