Hybrid sketching saves up to 97% space on dense graphs and 15% on sparse ones by sketching dense cores and storing sparse parts exactly, with new BalloonSketch reducing sketch sizes up to 8x.
Sketching as a Tool for Numerical Linear Algebra
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abstract
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. In this survey we consider least squares as well as robust regression problems, low rank approximation, and graph sparsification. We also discuss a number of variants of these problems. Finally, we discuss the limitations of sketching methods.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Deterministic sketching via row subset selection produces subspace embeddings with probability 1 for Krylov methods and yields performance comparable to randomized sketching for matrix functions, linear systems, and eigenvalue problems.
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Hybrid Sketching Methods for Dynamic Connectivity on Sparse Graphs
Hybrid sketching saves up to 97% space on dense graphs and 15% on sparse ones by sketching dense cores and storing sparse parts exactly, with new BalloonSketch reducing sketch sizes up to 8x.
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Deterministic sketching for Krylov subspace methods
Deterministic sketching via row subset selection produces subspace embeddings with probability 1 for Krylov methods and yields performance comparable to randomized sketching for matrix functions, linear systems, and eigenvalue problems.