matlab-線性方程組的迭代解法-GaussSeidel

1、精選優(yōu)質(zhì)文檔-傾情為你奉上實(shí)驗(yàn)1：線性方程組的迭代解法專業(yè)班級(jí)學(xué)號(hào)姓名實(shí)驗(yàn)日期1、實(shí)驗(yàn)環(huán)境MATLAB2009A2、實(shí)驗(yàn)?zāi)康暮鸵竽康模豪肎auss-Seidel編程法求解方程組要求：代碼能列出每一次迭代的中間值3、解題思路、代碼3.1解題思路 Gauss-Seidel迭代公式：xi(k+1)=(bi-aijxj(k+1)- aijxj(k)/aij (i=1,2,n)3.2 代碼function x = GaussSeidel(A, b, es, maxit)% GaussSeidel: Gauss Seidel method% x = GaussSeidel(A, b):Gauss Se

2、idel without relaxation% input:% A = coefficient matrix% b = right hand side vector% es = stop criterion(default = 0.00001%)% maxit = max iteration (default = 50)% output:% x = solution vector if nargin < 2, error('at least 2 input arguments required'), endif nargin<4 | isempty(maxit),

3、 maxit=50; endif nargin<3 | isempty(es), es=0.00001; endk=0xk=0 0 0 0 m, n = size(A);if m=n, error('Matrix A must be square'); endC = A;for i = 1:n C(i,i) = 0; x(i) = 0;endx = x'for i = 1:n C(i,1:n) = C(i,1:n)/A(i,i);end for i = 1:n d(i) = b(i)/A(i,i);end iter = 0;while(1) xold = x; f

4、or i = 1:n x(i) = d(i)-C(i,:)*x; if x(i) = 0 ea(i) = abs(x(i)-xold(i)/x(i) * 100; end endk=k+1xk=x'%此行不打分號(hào)，并且轉(zhuǎn)置，以便于輸出每次迭代的結(jié)果 iter=iter + 1; if (max(ea)<=es | iter = maxit) break; endend end4、實(shí)驗(yàn)步驟4.1輸入：4.2輸出：.5、討論和分析GaussSeidel迭代法是通過利用xi(k+1)=(bi-aijxj(k+1)- aijxj(k)/aij (i=1,2,n)這個(gè)公式，經(jīng)過若干次運(yùn)算，使結(jié)果越來越逼近方程的真實(shí)解。實(shí)驗(yàn)的重點(diǎn)是代碼中如何實(shí)現(xiàn)迭代公式以及代碼中控制好循環(huán)。GaussSeidel迭代法，是jacobi迭代法的改進(jìn)，將剛算