Improved Lower Bounds for the Maximum Growth Factor in Gaussian Elimination with Complete Pivoting
The maximum growth factor under complete pivoting is larger than 1.0045n for all n > 10, and the lim sup of the ratio with n is greater than or equal to 3.317. This disproves the long-standing conjecture that the growth factor is at most n.
Randomized Nyström Approximation for Low-Rank Approximation of Non-Negative Self-Adjoint Operators
This paper presents an infinite-dimensional extension of the randomized Nyström approximation to compute low-rank approximations of non-negative self-adjoint trace-class operators. The analysis yields bounds on the expected value and tail bounds for the Nyström approximation error in the operator, trace, and Hilbert-Schmidt norms.
Convergence Analysis of Quantile Randomized Kaczmarz Method for Linear Systems with Time-Varying Noise and Corruption
The Quantile Randomized Kaczmarz (QRK) method converges at least linearly in expectation up to a convergence horizon even when the linear system is perturbed by time-varying noise and corruption. The rate of convergence depends only on the corruption rate, while the convergence horizon depends on both the corruption rate and the time-varying noise.
Randomized Matrix Computations: Themes and Variations
This content delves into the application of randomized algorithms in numerical linear algebra, focusing on matrix computations and approximation methods.
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