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In this paper, we introduce a parallel implementation of a numerical verification method for generalized Hermitian eigenvalue problems to compute rigorous error bounds for eigenvectors and eigenvalues in a prescribed domain. The verification method is based on the Sakurai-Sugiura method that has hierarchical parallelism and fully utilizes the performance by parallel implementation. We implement a rigorous version of the Sakurai-Sugiura method using the Julia language and evaluate its performance. This paper provides the development in the fields of mechanics and electromagnetics etc. because it reduces the computation time, while computes error bounds rigorously for eigenvectors and eigenvalues.

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Parallel Implementation of a Verified Contour Integral Based Eigensolver and Its Performance Evaluation Using the Julia Language

  • 会议论文

  • 发表日期：

    2025年

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  • Shota Seto,
  • Akitoshi Takayasu

摘要

In this paper, we introduce a parallel implementation of a numerical verification method for generalized Hermitian eigenvalue problems to compute rigorous error bounds for eigenvectors and eigenvalues in a prescribed domain. The verification method is based on the Sakurai-Sugiura method that has hierarchical parallelism and fully utilizes the performance by parallel implementation. We implement a rigorous version of the Sakurai-Sugiura method using the Julia language and evaluate its performance. This paper provides the development in the fields of mechanics and electromagnetics etc. because it reduces the computation time, while computes error bounds rigorously for eigenvectors and eigenvalues.