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Parallel Generalized Real Symmetric-Definite Eigenvalue Problem.

James S Sims1, María Bélen Ruiz2

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.

Journal of Research of the National Institute of Standards and Technology
|September 23, 2024
PubMed
Summary
This summary is machine-generated.

This paper introduces a fast, portable parallel software package for solving large generalized real symmetric-definite eigenvalue problems. It efficiently handles dense matrices exceeding 80,000x80,000 dimensions.

Keywords:
dense matrix eigensolverhigh precisionparallel

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Area of Science:

  • Numerical Analysis
  • High-Performance Computing
  • Linear Algebra

Background:

  • Solving large-scale eigenvalue problems is computationally intensive.
  • Existing methods may lack efficiency or portability for massive datasets.

Purpose of the Study:

  • To present a novel software package for generalized real symmetric-definite eigenvalue problems (GRSDEP).
  • To enable efficient computation on large, dense matrices using parallel processing.

Main Methods:

  • Development of a Fortran 90+ package utilizing quadruple precision.
  • Implementation of portable parallel algorithms for GRSDEP.
  • Optimization for matrices of size 80,000x80,000 or greater.

Main Results:

  • The package demonstrates computational speed suitable for large-scale problems.
  • Achieved portability across different parallel computing architectures.
  • Successfully handles dense matrices beyond typical computational limits.

Conclusions:

  • The developed GRSDEP package offers a significant advancement in solving large eigenvalue problems.
  • It provides a fast, portable, and efficient solution for researchers and engineers dealing with massive dense matrices.