Random orthonormal matrices are minimax optimal for sketched least squares and rotation-invariant embeddings for randomized SVD, yielding the sharpest error bounds.
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Accelerates the power method for extracting top principal components using fast sketching and regularized spectral approximation for stronger low-rank guarantees.
A multilevel sketch-and-solve estimator reduces variance faster than averaging independent sketches but incurs slightly higher computational cost, making the approach unattractive for least squares problems.
Combines polynomial codes and randomized sketching into approximate distributed schemes that mitigate stragglers during optimization and machine learning tasks.
A unified randomized batch-sampling Kaczmarz framework yields scale-invariant expected linear convergence bounds for block methods solving linear systems.
Flexible GMRES stabilizes sketched GMRES through a new residual bound, producing a practical randomized solver with minimal tuning and robust non-increasing residual norms.
Direct SVD solves coupled decompositions; randomized versions with novel balanced subspace selection improve efficiency and apply to face recognition.
PEPSKit.jl is a Julia package that supplies high-level algorithms for ground-state, time-evolution and finite-temperature iPEPS simulations with symmetry support on various lattices.
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Randomized coupled decompositions
Direct SVD solves coupled decompositions; randomized versions with novel balanced subspace selection improve efficiency and apply to face recognition.