Routines for eigenvalue and singular value computations
Some of the routines are part as software from publications. Others are put here to test algorithms and so forth.
- Reductions and factorizations of tridiagonal matrices,
- CTR (not yet available): Orthogonal reduction to tridiagonal form
- BTR (not yet available): Build the tridiagonal matrix based on the diagonal and subdiagonal
- MULT (April 01 2010 10:21:20): Multiply a tridiagonal matrix fast with a vector
- CHOLT (April 01 2010 10:21:20): Compute the Cholesky decomposition of a tridiagonal matrix
IMPORTANT REMARK: THE ROUTINES PRESENTED BELOW FOR COMPUTING THE GENERALIZED DEFINITE EIGENPROBLEM ARE NOT THE MOST UP TO DATE ONES.
THE NEW ONES ARE MUCH BETTER W.R.T. TIMINGS AND ACCURACY.
THEY WILL BE POSTED HERE AS SOON AS POSSIBLE. If you intend to use these files, you can request me a copy.
- Definite Generalized symmetric Tridiagonal Eigenvalue problem (Computing the generalized eigenvalues/vectors)
Reduction via unitary equivalence to bidiagonal form.
- DGSTE (April 01 2010 10:21:16): solve the Definite Generalized Symmetric Tridiagonal Eigenvalue problem
- LTL (April 01 2010 10:21:16): compute L^(-1) T L^(-T), with T and S=LL^T tridiagonal matrices
- BQ (April 01 2010 10:21:07): Build full Quasiseparable matrix (works on the output of LTL)
- DCQGV (April 01 2010 10:21:16): Divide and Conquer for a Quasiseparable Givens-Vector represented matrix
Takagi factorization or symmetric singular value decomposition.
- BiDiag (April 01 2010 10:21:20): Unitary equivalence to bidiagonal form.
- TestBiDiag (April 01 2010 10:21:20): Test the above routine.
Eigenvalues of tridiagonal plus rank one matrices.
Eigenvalues of the Hatano-Nelson Transition Matrix.
- Takagi (not yet available): Compute the Takagi factorization of a complex symmetric matrix.
- TestTakagi (not yet available): Test the above m file..
- Unfortunately not yet available, an unpolished version can be obtained from the author when requested via email.