The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows us to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.


  1. generalized eigenproblem
  2. FEAST
  3. quadrature
  4. Zolotarev
  5. filter design
  6. load balancing

MSC codes

  1. 65F15
  2. 41A20
  3. 65Y05

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A2100 - A2122
ISSN (online): 1095-7197


Submitted: 30 July 2014
Accepted: 8 June 2015
Published online: 18 August 2015


  1. generalized eigenproblem
  2. FEAST
  3. quadrature
  4. Zolotarev
  5. filter design
  6. load balancing

MSC codes

  1. 65F15
  2. 41A20
  3. 65Y05



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