We study last-iterate convergence of SGD with greedy step size over smooth quadratics in the interpolation regime, a setting which captures the classical Randomized Kaczmarz algorithm as well as other popular iterative linear system solvers. For these methods, we show that the $t$-th iterate attains an $O(1/t^{3/4})$ convergence rate, addressing a question posed by Attia, Schliserman, Sherman, and Koren, who gave an $O(1/t^{1/2})$ guarantee for this setting. In the proof, we introduce the family of stochastic contraction processes, whose behavior can be described by the evolution of a certain deterministic eigenvalue equation, which we analyze via a careful discrete-to-continuous reduction.

Moreoverkappr K, is squared FrkapproximationA, i.e., min Examining 3, left), it sharperpeakk, whereas resultsinthe1.

Finally, we extend LESS embeddings to include uniformly sparsified random sign matrices which canbeimplemented efficiently andwhich perform wellinnumericalexperiments.

Finally, we extend LESS embeddings to include uniformly sparsified random sign matrices which canbeimplemented efficiently andwhich perform wellinnumericalexperiments.

Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation - indeed worse than some i.i.d.

Matrix sketching is a powerful tool for reducing the size of large data matrices.