Fast Computation of a Restricted Subset of Eigenpairs of a Varying Hermitian Matrix

  • Pierre Comon
Part of the NATO ASI Series book series (volume 70)


Standard algorithms require an order of dm 2 flops to compute d eigenpairs of a m × m semi-definite positive hermitian matrix, R. A larger amount of computations (of same order) is required to find d left singular pairs of a square matrix, D, such that R = DD H ; this is known to be numerically more stable. Note that D is not unique, the best choice in the sequel turns out not to be the Cholesky factor of R. The algorithm proposed in this contribution will compute d left singular pairs of D in a faster way, such that it requires an order of αmd 2 flops. This algorithm takes advantage of the fact that the matrix considered is nothing else but a matrix whose d eigenpairs are known, perturbed by a rank-one modification. It is pointed out in the sequel why the technique of Bunch et al [1] is not relevant for O(md 2) algorithms, neither for square-root implementations.


Cholesky Factor Ritz Vector Subspace Iteration Positive Definite Hermitian Matrix Singular Triplet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Pierre Comon
    • 1
  1. 1.Thomson Sintra, ASMCagnes sur merFrance

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