fddfebs.m

五对角线性方程组求解程序. 速度奇快.一千阶,0.019秒 一万阶:0.56秒 10万阶:61秒. 数据输入结构见程序内英文说明.

function x=fddfebs(a,b,c,d,e,f)
% x=fddfebs(a,b,c,d,e,f)
%    This is a function to solve five-diagonal dominantly linear eqations
%    system    Ax=f.
% input data:
%    a is 1xn array with n-2 data, the data is start at
%    the 3rd,it is the down second diagonal line data.
%    b is 1xn array with n-1 data, the data is start at
%    the 2nd,it is the down first diagonal line data.
%    c is 1xn array with n data, the data is start at
%    the 1st,it is the main diagonal line data.
%    d is 1xn array with n-1 data, the data is start at
%    the 1st,it is the up first diagonal line data.
%    e is 1xn array with n-2 data, the data is start at
%    the 1st,it is the up second diagonal line data.
%    f is nx1 array with n data, the data is start at
%    the 1st,it is the right vector of the equations.
% output data:
%    x is the solution of the linear eqations system, it is 1xn.

n=size(f,1);

alph=zeros(1,n);
beta=zeros(1,n);
gamma=zeros(1,n);
z=zeros(1,n);
q=zeros(1,n);
if size(c,2)~=n
    error('Error size of data!');
end
alph(1)=c(1);
beta(1)=d(1)/alph(1);
gamma(2)=b(2);
alph(2)=c(2)-gamma(2)*beta(1);
y(1)=f(1)/alph(1);
y(2)=(f(2)-gamma(2)*y(1))/alph(2);
for k=1:n-2
    q(k)=e(k)/alph(k);
    beta(k+1)=(d(k+1)-gamma(k+1)*q(k))/alph(k+1);
    
    %z(k+2)=a(k+2);
    gamma(k+2)=b(k+2)-a(k+2)*beta(k);
    alph(k+2)=c(k+2)-a(k+2)*q(k)-gamma(k+2)*beta(k+1);
    y(k+2)=(f(k+2)-a(k+2)*y(k)-gamma(k+2)*y(k+1))/alph(k+2);
end
clear alph;clear gamma;clear a;clear b;clear c;clear d;clear e;clear f;
x(n)=y(n);
x(n-1)=y(n-1)-beta(n-1)*x(n);
for k=n-2:-1:1
    x(k)=y(k)-q(k)*x(k+2)-beta(k)*x(k+1);
end
return