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Residual algorithm for large-scale positive definite generalized eigenvalue problems

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Abstract

In the positive definite case, the extreme generalized eigenvalues can be obtained by solving a suitable nonlinear system of equations. In this work, we adapt and study the use of recently developed low-cost derivative-free residual schemes for nonlinear systems, to solve large-scale generalized eigenvalue problems. We demonstrate the effectiveness of our approach on some standard test problems, and also on a problem associated with the vibration analysis of large structures. In our numerical results we use preconditioning strategies based on incomplete factorizations, and we compare with and without preconditioning with a well-known available package.

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Authors and Affiliations

  1. Departamento de Matemática, FaCyT, Universidad de Carabobo, Valencia, Venezuela

    Lenys Bello

  2. Departamento de Electrónica, Computación y Control, Escuela de Ingeniería Eléctrica, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas, 1051-DF, Venezuela

    William La Cruz

  3. Departamento de Cómputo Científico y Estadística, Universidad Simón Bolívar (USB), Ap. 89000, Caracas, 1080-A, Venezuela

    Marcos Raydan

Authors
  1. Lenys Bello
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  2. William La Cruz
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  3. Marcos Raydan
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Corresponding author

Correspondence to Marcos Raydan.

Additional information

Dedicated with friendship to José Mario Martínez for his outstanding scientific contributions.

William La Cruz was supported by CDCH-UCV project PI-08-7276-2008/1.

Marcos Raydan was supported by USB and the Scientific Computing Center at UCV.

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Bello, L., La Cruz, W. & Raydan, M. Residual algorithm for large-scale positive definite generalized eigenvalue problems. Comput Optim Appl 46, 217–227 (2010). https://doi.org/10.1007/s10589-009-9250-9

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  • DOI: https://doi.org/10.1007/s10589-009-9250-9

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