Given a tridiagonal matrix, sets small off-diagonal elements to zero and for each unreduced block, finds base representations and eigenvalues.
To find the desired eigenvalues of a given real symmetric tridiagonal matrix
?larre2asets any "small" off-diagonal elements to zero, and for each unreduced block
, it finds
- a suitable shift at one end of the block's spectrum,
- the base representation,T-iσiI=LiDiLiT, and
- eigenvalues of eachLiDiLiT.
The algorithm obtains a crude picture of all the wanted eigenvalues (as selected by
range). However, to reduce work and improve scalability, only the eigenvalues
douare refined. Furthermore, if the matrix splits into blocks, RRRs for blocks that do not contain eigenvalues from
douare skipped. The DQDS algorithm (
subroutine) is not used, unlike in the sequential case. Instead, eigenvalues are computed in parallel to some figures using bisection.
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
- CHARACTER= 'A': ("All") all eigenvalues will be found.= 'V': ("Value") all eigenvalues in the half-open interval (vl,vu] will be found.= 'I': ("Index")thewill be found.il-th throughiu-th eigenvalues (of the entire matrix)
- INTEGERThe order of the matrix.n> 0.