Lanczos
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Related Articles from SNS
A structural bound for cluster robustness of randomized small-block Lanczos
Announce Type: replace Abstract: The Lanczos method is a fast and memory-efficient algorithm for solving large-scale symmetric eigenvalue problems. However, its rapid convergence can deteriorate significantly when computing clustered eigenvalues due to a lack of cluster robustness. A promising strategy to enhance cluster robustness -- without substantially compromising convergence speed or memory efficiency -- is to use a random small-block initial, where the block size is greater than one...
Optimal Stochastic Krylov based Techniques for Large- Scale Log-Determinant Estimation
arXiv:2606.07004v1 Announce Type: new Abstract: Estimating the logarithm of the determinant of large sparse positive definite symmetric matrices is an important task in numerical linear algebra, machine learning, Gaussian processes, and uncertainty quantification. In this work, we introduce two scalable and efficient methods for large-scale log-determinant termed the Optimal Stochastic Arnoldi with Incomplete Orthogonalization Procedure (OSA-IOP) and the Optimal Stochastic Lanczos Quadrature...
A Perturbed q-Tsallis Self-Concordant Barrier for Spectrally Robust Semidefinite Programming
Announce Type: cross Abstract: We introduce and analyse a perturbed $q$-Tsallis barrier for semidefinite programming (SDP), defined as a spectral perturbation of the classical log-det barrier on the cone of positive definite matrices. The barrier introduces eigenvalue-adaptive stiffening through a Tsallis-type matrix-power term controlled by parameters $q>1$ and $\eta\geq0$. Our main theoretical contribution is a sharp characterisation of the differential self-concordance regime of the...