
Matrix pencils with coefficients that have positive semidefinite Hermitian part
We analyze when an arbitrary matrix pencil is equivalent to a dissipativ...
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On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix
Lower bounds on the smallest eigenvalue of a symmetric positive definite...
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Uniform Error Estimates for the Lanczos Method
The Lanczos method is one of the most powerful and fundamental technique...
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A lower bound on the positive semidefinite rank of convex bodies
The positive semidefinite rank of a convex body C is the size of its sma...
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An OptimalStorage Approach to Semidefinite Programming using Approximate Complementarity
This paper develops a new storageoptimal algorithm that provably solves...
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A Strengthening of the PerronFrobenius Theorem
It is well known from the PerronFrobenius theory that the spectral gap ...
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A New Proof of Hopf's Inequality Using a Complex Extension of the Hilbert Metric
It is well known from the PerronFrobenius theory that the spectral gap ...
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Accuracy of approximate projection to the semidefinite cone
When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking standard eigenvalue perturbation theory (e.g. DavisKahan and Weyl bounds) suggests that the accuracy would be inversely proportional to the spectral gap, implying it can be poor in the presence of small eigenvalues. This work shows that a small gap is not a concern for projection onto the semidefinite cone, by deriving error bounds that are gapindependent.
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