MATLAB-现代控制理论-法捷耶娃法

在网上找到了一个单似乎不是很好用，所以就改良了一下，法捷耶娃法求矩阵(sI-A)的逆
function [a,ainv,c,b,n]=fadlev1(a)
%
% fadlev  faddeev-leverrier approach to generate coefficients of the
% characteristic polynomial and inverse of a given matrix
% uasage:        [p,ainv,b]=fedlev(a)
%
% input:     a - the given matrix
% output:    a - the coefficient vector of the characteristic polynomial
%            c - a cell array of the sequency of matrices generated, where
%               c{1} = a                    p(1)=trace(c{1})
%               c{2} = a*(c{1}-p(1)*i)      p(2)=trace(c{2})/2
%               .....
%               c{n} = a*(c{n-1}-p(n-1)*i)  p(n)=trace(c{n})/n
%            b-法捷耶娃法中的伴随矩阵算子
%            n-所求伴随矩阵
%           ainv - the inverse of a calculated as
%               ainv = (c{n-1}-p(n-1)*i)/p(n)
%
%
%
[n,m]=size(a);
if n~=m
   error(the given matrix is not square!);
end
[c{1:n}]=deal(a);
a=ones(1,n+1);
b{1}=eye(n);
for k=2:n
   a(k)=-trace(c{k-1})/(k-1);
   c{k}=a*(c{k-1}+a(k)*eye(n));
   b{k}=c{k}*inv(a);
end
a(n+1)=-trace(c{n})/n;
ainv=-(c{n-1}+a(n)*eye(n))/a(n+1);
syms s
n=0
for i=1:n
n=n+b{i}*s^(n-i)
end
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原文地址： Http://blog.gkong.com/more.asp?id=83974&Name=psychekklll