Extended Eigensolver Functionality

The eigenvalue problems covered are as follows:

• standard, Ax = λx

  • A complex Hermitian

  • A real symmetric

• generalized, Ax = λBx

  • A complex Hermitian, B Hermitian positive definite (hpd)

  • A real symmetric and B real symmetric positive definite (spd)

The Extended Eigensolver functionality offers:

• Real/Complex and Single/Double precisions: double precision is recommended to provide better accuracy of eigenpairs.

• Reverse communication interfaces (RCI) provide maximum flexibility for specific applications. RCI are independent of matrix format and inner system solvers, so you must provide your own linear system solvers (direct or iterative) and matrix-matrix multiply routines.

• Predefined driver interfaces for dense, LAPACK banded, and sparse (CSR) formats are less flexible but are optimized and easy to use:

  • The Extended Eigensolver interfaces for dense matrices are likely to be slower than the comparable LAPACK routines because the FEAST algorithm has a higher computational cost.

  • The Extended Eigensolver interfaces for banded matrices support banded LAPACK-type storage.

  • The Extended Eigensolver sparse interfaces support compressed sparse row format and use the Intel® oneAPI Math Kernel Library PARDISO solver.

• Parallelism in Extended Eigensolver Routines
  
• Achieving Performance With Extended Eigensolver Routines