Numerical Algorithms

, Volume 66, Issue 4, pp 681–703 | Cite as

An indefinite variant of LOBPCG for definite matrix pencils

  • Daniel Kressner
  • Marija Miloloža Pandur
  • Meiyue ShaoEmail author
Original Paper


In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil \(A-\lambda B\), that is, A, B are Hermitian and there is a shift \(\lambda _{0}\) such that \(A-\lambda _{0} B\) is definite. Our new method can be seen as a variant of the popular LOBPCG method operating in an indefinite inner product. It also turns out to be a generalization of the recently proposed LOBP4DCG method by Bai and Li for solving product eigenvalue problems. Several numerical experiments demonstrate the effectiveness of our method for addressing certain product and quadratic eigenvalue problems.


Eigenvalue Definite matrix pencil Minimization principle LOBPCG 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Kressner
    • 1
  • Marija Miloloža Pandur
    • 1
    • 2
  • Meiyue Shao
    • 1
    Email author
  1. 1.ANCHP, MATHICSE, EPF LausanneLausanneSwitzerland
  2. 2.Department of MathematicsJ. J. Strossmayer University of OsijekOsijekCroatia

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