Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

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TimeEvolver: A program for time evolution with improved error bound

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We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

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In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

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Iterative refinement of Schur decompositions

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The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

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