I am interested in studying the eigenvalues and eigenvectors of a 'large' matrix (say $1000\times1000$) that depends on two parameters $x$ and $y$. Let's refer to this matrix as


where $n$ is the size and $x, y$ are the previously mentioned parameters. I would like to create a 'master' table of Eigensystem[BigMatrix[1000,x,y]] for many values of $x,y$ and export it so I don't have to rerun these Eigensystem commands all the time. I have tried

Export["BigTable.mx",Table[Eigensystem[BigMatrix[1000, j/100, k/100]], {j, 
   0, 100, 1}, {k, 0, 100, 1}]];

but Mathematica seems to stop working when I leave it running overnight. Is there a more efficient way? Or should I be exporting Eigensystem[BigMatrix[1000,x,y]] for each value of $x$ and $y$?

Thanks for your suggestions.

  • $\begingroup$ You are trying to put 100*100 very large results in a file. I would think about putting each result in its own file. That way at least: 1. You'll get a good idea of how long it will take to complete. 2. You can restart it if you run into problems part way through. 3. You reduce the risk of running out of memory. $\endgroup$
    – mikado
    Oct 29, 2022 at 21:45
  • $\begingroup$ Use Put or PutAppend after each eigensystem is calculated. $\endgroup$ Oct 30, 2022 at 8:01
  • $\begingroup$ Thank you! I was not aware of the PutAppend command. $\endgroup$
    – Elliot
    Oct 30, 2022 at 19:49


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