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### [Lapack] What is the biggest size of a real symmetric tridiagonal matrix

 ``` On Oct 2, 2012, at 6:28 AM, Leonardo Castelano wrote: ``````I need to diagonalize a real symmetric tridiagonal matrix, which should be as big as possible. So my questions regarding this subject are: (1) What is the biggest size of a matrix that LAPACK is able to diagonalize? `````` Depends if you want eigenvalues only or eigenvalues and eigenvectors. I assume that by diagonalizing you want both (eigenvalues and eigenvectors) in which case, you are essentially limited by your memory. (Since the matrix of eigenvectors is dense, this will be your bottleneck.) Typically 20K starts to be big big matrices. You can always try to push. If the matrix is symmetric tridiagonal and you only want the eigenvalues, 1) the computation is extremely fast, and 2) the storage is low. I have no idea how much people pushed LAPACK in these conditions. I would assume we can handle eigenvalue computation for symmetric tridiagonal matrices of size above one million without too much problems. ``````(2) Which subroutine should I use? `````` You want to look at all the routines which starts by DSTE___ (or SSTE___ ) (DSTE stands for Double Presicion, Symmetric, Tridiagonal, Eigenvalue.) We have four algorithms in place so there is quite a collection there. DSTEQR, QR method DSTEMR, MRRR method DSTEDC, Divide and Conquer method DSTEGR: deprecated etc. Cheers, Julien. ```
 Current Thread [Lapack] What is the biggest size of a real symmetric tridiagonal matrix that LAPACK is able to diagonalize?, Leonardo Castelano [Lapack] What is the biggest size of a real symmetric tridiagonal matrix that LAPACK is able to diagonalize?, Langou, Julien <=

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