Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

Nonsymmetric Eigenvalue Problems: ScaLAPACK Computational Routines

This section describes ScaLAPACK routines for solving nonsymmetric eigenvalue problems, computing the Schur factorization of general matrices, as well as performing a number of related computational tasks.
To solve a nonsymmetric eigenvalue problem with ScaLAPACK, you usually need to reduce the matrix to the upper Hessenberg form and then solve the eigenvalue problem with the Hessenberg matrix obtained.
Table
"Computational Routines for Solving Nonsymmetric Eigenproblems"
lists ScaLAPACK routines for reducing the matrix to the upper Hessenberg form by an orthogonal (or unitary) similarity transformation
A
=
QHQ
H
, as well as routines for solving eigenproblems with Hessenberg matrices, and multiplying the matrix after reduction.
Computational Routines for Solving Nonsymmetric Eigenproblems
Operation performed
General matrix
Orthogonal/Unitary matrix
Hessenberg matrix
Reduce to Hessenberg form
A
=
QHQ
H
 
 
Multiply the matrix after reduction
 
 
Find eigenvalues and Schur factorization
 
 

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