Proves relative-gap-preserving error bounds for singular vectors and eigenvectors from mixed-precision Jacobi methods that depend on the preconditioned matrix scaled condition number rather than the original.
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Matrix Analysis
19 Pith papers cite this work. Polarity classification is still indexing.
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Formalizes pre-data effective sample size for GGMs under Wishart and G-Wishart priors and introduces DPIR and BFDA extensions for sample size planning.
Greedy vector balancing on finite unit-vector sets T in R^d achieves norm bound (2/δ_T)^{d-1} independent of sequence length n.
A Gaussian mean width bound in weighted geometry yields a single-letter strong converse for the classical identification capacity of quantum channels, improving known results for depolarizing, Pauli, erasure, and amplitude damping channels.
Presents a quantum soft PCA framework with Fermi-Dirac filter for principal subspace scoring without eigenvector recovery, claiming dimension-independent sample complexity O(η^{-2}).
Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
Optimal O(n^{-1/2}) convergence in trace distance with third moments and O(n^{-1}) in relative entropy with fourth moments for the quantum CLT in m-mode bosonic systems.
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Witness motifs in constrained geometric graphs saturate Weyl bounds on Laplacian perturbations under heavy-tailed noise, with new metrics SC and S3I to distinguish noise-driven spectral effects.
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).
Alternative adiabatic dynamics implementable via discrete gates on quantum computers yield optimal QLSP algorithms and improved randomized Trotter bounds.
A Jacobi-like eigenvalue algorithm for real normal matrices that accelerates via the skew-symmetric part and Paardekooper's method, plus formulas for related nearest-matrix problems.
citing papers explorer
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Computing accurate singular vectors and eigenvectors using mixed-precision Jacobi algorithms
Proves relative-gap-preserving error bounds for singular vectors and eigenvectors from mixed-precision Jacobi methods that depend on the preconditioned matrix scaled condition number rather than the original.
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What is your Prior Worth? Effective Sample Size and Sample Size Planning for Gaussian Graphical Models
Formalizes pre-data effective sample size for GGMs under Wishart and G-Wishart priors and introduces DPIR and BFDA extensions for sample size planning.
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Greedy Vector Balancing
Greedy vector balancing on finite unit-vector sets T in R^d achieves norm bound (2/δ_T)^{d-1} independent of sequence length n.
-
Gaussian mean width strong converse bound on the classical identification capacity of quantum channels
A Gaussian mean width bound in weighted geometry yields a single-letter strong converse for the classical identification capacity of quantum channels, improving known results for depolarizing, Pauli, erasure, and amplitude damping channels.
-
Quantum principal component analysis without eigenvector recovery
Presents a quantum soft PCA framework with Fermi-Dirac filter for principal subspace scoring without eigenvector recovery, claiming dimension-independent sample complexity O(η^{-2}).
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Expected hyperbolic volumes of random beta polytopes
Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
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GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression
GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
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Optimal convergence rates in trace distance and relative entropy for the quantum central limit theorem
Optimal O(n^{-1/2}) convergence in trace distance with third moments and O(n^{-1}) in relative entropy with fourth moments for the quantum CLT in m-mode bosonic systems.
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Doubly minimized Petz and sandwiched Renyi mutual information: Properties
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
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Anchor PCA
Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
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Error bounds for approximate posteriors from likelihood-informed reduced-order models
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Spectral Effects Of Heavy-Tailed Vertex Noise In Geometric Graphs
Witness motifs in constrained geometric graphs saturate Weyl bounds on Laplacian perturbations under heavy-tailed noise, with new metrics SC and S3I to distinguish noise-driven spectral effects.
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Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
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Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).
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Alternative adiabatic quantum dynamics with algorithmic applications
Alternative adiabatic dynamics implementable via discrete gates on quantum computers yield optimal QLSP algorithms and improved randomized Trotter bounds.
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A Jacobi-like algorithm for normal matrices by the skew-symmetric part
A Jacobi-like eigenvalue algorithm for real normal matrices that accelerates via the skew-symmetric part and Paardekooper's method, plus formulas for related nearest-matrix problems.
- On Matricial Order Operator Spaces
- On generalization of Williamson's theorem to real symmetric matrices