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A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

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  • F. Abbasi Nedamani
  • A. H. Refahi Sheikhani
  • H. Saberi Najafi

Abstract

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods.

Suggested Citation

  • F. Abbasi Nedamani & A. H. Refahi Sheikhani & H. Saberi Najafi, 2020. "A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, December.
    • Handle: RePEc:hin:jnlmpe:8895856
    DOI: 10.1155/2020/8895856
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