An O(n)-randomness perturbation combining a dense deterministic pattern matrix with a non-uniform sparse dependent perturbation reduces condition numbers to O(n) for any input matrix.
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2026 3verdicts
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OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.
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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Well-Conditioned Oblivious Perturbations in Linear Space
An O(n)-randomness perturbation combining a dense deterministic pattern matrix with a non-uniform sparse dependent perturbation reduces condition numbers to O(n) for any input matrix.
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Oblivious Subspace Injection Is Not Enough for Relative Error
OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.
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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.