R. Kunsch

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math.NA2026

Sharp bounds for non-adaptive randomized approximation of high-dimensional noisy vectors

Robert J. Kunsch, Marcin Wnuk

We study the complexity of approximating the finite-dimensional vector space embedding $ℓ_{p}^{m} ↪ ℓ_{q}^{m}$ for $2 \leq p < q \leq \infty$ based on non-adaptive rand…

math.NA2025

Adaptive and non-adaptive randomized approximation of high-dimensional vectors

Robert J. Kunsch, Marcin Wnuk

We study approximation of the embedding $ℓ_{p}^{m} ↪ ℓ_{q}^{m}$ , $1 \leq p < q \leq \infty$ , based on randomized algorithms that use up to $n$ arbitrary linear function…

math.NA2024

Uniform approximation of vectors using adaptive randomized information

Robert J. Kunsch, Marcin Wnuk

We study approximation of the embedding $ℓ_{p}^{m} \to ℓ_{\infty}^{m}$ , $1 \leq p \leq 2$ , based on randomized adaptive algorithms that use arbitrary linear functionals as…

math.NA2024

Randomized approximation of summable sequences -- adaptive and non-adaptive

Robert Kunsch, Erich Novak, Marcin Wnuk

We prove lower bounds for the randomized approximation of the embedding $ℓ_{1}^{m} \to ℓ_{\infty}^{m}$ based on algorithms that use arbitrary linear (hence non-adaptive) info…