i would like to consider singular value decomposition of such type of matrix
creation of matrix from small sample is not big issue, i have ready code for this
function [x ]=create_matrix(b,l) %This Function is used to Create Hankel Type Data Matrix %x is a given data %l represent window size n = length(b); m = n-l+1; x = zeros(m,l); for i=1:m x(i,:)=b(i:i+l-1); end
but when i have huge data , for instance time series with sample size of 500000 and more, then creation of matrix will make computer unresponsive, i have searched in internet articles related to this topic and found following resource
efficient singular value decomposition
but problem is ,that before applying given algorithm , i should create matriix itself, my research is about to create step by step approximation of SVD, instead of creation huge matrix, can i create small matrices in process, calculate svd of given matrix and after loop operations , get result as the svd of huge matrix?let me clarify my question :
suppose i want create matrix with size of $n$ by $m$ which both $n$ and $m$ are hug numbers, what i am doing is choose small $p$ and $k$ and creating matrix $p$ by $k$, i will calculate svd of given matrix, then i will update both $p$ and $k$ by $1$ unit and repeat again process, can i approximate svd of original matrix?please help me what to do?