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i would like to consider singular value decomposition of such type of matrix

enter image description here

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?

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This problem of updating the singular value decomposition of a matrix upon repeatedly appending a row or a column to the matrix is discussed in A stable and fast algorithm for updating the singular value decomposition.

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  • $\begingroup$ i hope that i will be able to understood it or at least to write code, could you tell me please a short summary about this process? what is general idea $\endgroup$ – dato datuashvili Oct 27 '17 at 14:50
  • $\begingroup$ it's an old method (1994), used by many since, you'll probably want to search for a ready-made code. $\endgroup$ – Carlo Beenakker Oct 27 '17 at 15:52
  • $\begingroup$ i think i need several days to clarify process itself $\endgroup$ – dato datuashvili Oct 27 '17 at 17:48

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