Contents

# Symmetric Eigenvalue Problems: ScaLAPACK Computational Routines

To solve a symmetric eigenproblem with ScaLAPACK, you usually need to reduce the matrix to real tridiagonal form
T
and then find the eigenvalues and eigenvectors of the tridiagonal matrix
T
. ScaLAPACK includes routines for reducing the matrix to a tridiagonal form by an orthogonal (or unitary) similarity transformation
A
=
QTQ
H
as well as for solving tridiagonal symmetric eigenvalue problems. These routines are listed in Table
"Computational Routines for Solving Symmetric Eigenproblems"
.
There are different routines for symmetric eigenproblems, depending on whether you need eigenvalues only or eigenvectors as well, and on the algorithm used (either the
QTQ
algorithm, or bisection followed by inverse iteration).
Computational Routines for Solving Symmetric Eigenproblems
Operation
Dense symmetric/Hermitian matrix
Orthogonal/unitary matrix
Symmetric tridiagonal matrix
Reduce to tridiagonal form
A
=
QTQ
H

Multiply matrix after reduction

Find all eigenvalues and eigenvectors of a tridiagonal matrix
T
by a
QTQ
method

Find selected eigenvalues of a tridiagonal matrix
T
via bisection

Find selected eigenvectors of a tridiagonal matrix
T
by inverse iteration

*
This routine is described as part of auxiliary ScaLAPACK routines.

#### Product and Performance Information

1

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