matlab求多项式的根,matlab – 计算多个多项式的根

这是3种方法之间的比较：

>通过所有行的简单循环,使用每行的根.

>完全无循环的方法,基于YBE使用块对角矩阵的想法,

使用稀疏作为中间

>通过所有行的简单循环,但这次使用来自根的“内联”代码.

代码：

%// The polynomials

m = 15;

n = 8;

N = 1e3;

X = rand(m,n);

%// Simplest approach

tic

for mm = 1:N

R = zeros(n-1,m);

for ii = 1:m

R(:,ii) = roots(X(ii,:));

end

end

toc

%// Completely loopless approach

tic

for mm = 1:N

%// Indices for the scaled coefficients

ii = repmat(1:n-1:m*(n-1), n-1,1);

jj = 1:m*(n-1);

%// Indices for the ones

kk = bsxfun(@plus, repmat(2:n-1, m,1), (n-1)*(0:m-1).'); %'

ll = kk-1;

%// The block diagonal matrix

coefs = -bsxfun(@rdivide, X(:,2:end), X(:,1)).'; %'

one = ones(n-2,m);

C = full(sparse([ii(:); kk(:)], [jj(:); ll(:)],...

[coefs(:); one(:)]));

%// T