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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Richardson iteration achieves universal 1/k backward error on PSD systems, enabling O(n²/ε) solvers; MINBERR reaches O(1/k²) rate and O(n²/√ε) complexity, with empirical O(1/k) extension to general systems.
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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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Towards Universal Convergence of Backward Error in Linear System Solvers
Richardson iteration achieves universal 1/k backward error on PSD systems, enabling O(n²/ε) solvers; MINBERR reaches O(1/k²) rate and O(n²/√ε) complexity, with empirical O(1/k) extension to general systems.