Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A Deflation-Preconditioned Conjugate Gradient Method for Symmetric Eigenproblems

  • Published : 2002.12.01

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Abstract

A preconditioned conjugate gradient(PCG) scheme with the aid of deflation for computing a few of the smallest eigenvalues arid their corresponding eigenvectors of the large generalized eigenproblems is considered. Topically there are two types of deflation techniques, the deflation with partial shifts and an arthogonal deflation. The efficient way of determining partial shifts is suggested and the deflation-PCG schemes with various partial shifts are investigated. Comparisons of theme schemes are made with orthogonal deflation-PCG, and their asymptotic behaviors with restart operation are also discussed.

Keywords

References

  1. Numer. Math. v.9 New iterative methods for the solution of the eigenproblem W.W.Bradbury;R.Fletcher
  2. Comput. Struct. v.58 A multi-mesh, preconditioned conjugate gradient solver for eigenvalue problems in finite element models Y.Cho;Y.K.Yong
  3. Internat. J. Numer. Methods Engrg. v.39 Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems Y.T.Feng;D.R.J.Owen
  4. SIAM J. Sci. Comput. v.16 Nested iterations for symmetric eigenproblems G.Gambolati;G.Pini;M.Putti
  5. J. Comput. Phys. v.74 An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices G.Gambolati;G.Pini;F.Sartoretto
  6. Internet. J. Numer. Mathods Engrg v.37 A comparison of Lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems G.Gambolati;M.Putti
  7. Comput. Methods Appl. Mech. Engrg. An orthogonal accelerated deflation technique for large symmetric eigenproblems G.Gambolati;F.Sartoretto;P.Florian
  8. J. Comput. Phys. Numerical stability of update method for large symmetric eigenvalue probelem H.Jang
  9. Linear Algebra Appl. v.34 Simultaneous Rayleigh quotient minimization methods for Ax=λBx D.E.Longsine;S.F.McCormick
  10. Comp. Meth. appl. Mech.Engrg. v.62 A partial preconditioned conjugate gradient method for large eigenproblems M.Papadrakakis;M.Yakoumidakis
  11. The Symmetric Eigenvalue Problem B.N.Parlett
  12. Computational Methods in Optimization: A Unified Approach E.Polak
  13. Sparse Matrix Techniques Computaion of eigenvalues and eigenvectors A.Ruhe;V.A.Baker(ed.)
  14. J. Comput. Phys. v.81 Accelerated simultaneous iterations for large finite element eigenproblems F.Sartoretto;G.Pini;G.Gambolati
  15. ISNM v.96 Eigenvalue problems and preconditioning H.R.Schwarz
  16. Lecture Notes in Mathmatics v.968 H.R.Schwarz;J.Hinze(ed.)
  17. Comput. Methods Appl. Mech. Engrg. v.3 The eigenvalue problem (A-λB)x = 0 for symmetric matrices of high order H.R.Schwarz