From the 1 of 7 linked papers with an AI index.
7 papers
A Twin gradient method for unconstrained optimization
Anna De Magistris, Michiel E. Hochstenbach, Gerardo Toraldo
The paper introduces a Twin‑Step gradient method that runs two parallel gradient sequences and chooses step sizes to minimize the distance between them, with a hybrid fallback to a…
Transpose-free linear algebra
Diana Halikias, Michiel E. Hochstenbach, Alex Townsend
We study the limitations of matrix-free algorithms that access a matrix only through forward matrix-vector products (matvecs) , without access to the transpose $A…
Deterministic and randomized Kaczmarz methods for with applications to color image restoration
Wenli Wang, Duo Liu, Gangrong Qu +1
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy…
On spectral properties and fast initial convergence of the Kaczmarz method
Per Christian Hansen, Michiel E. Hochstenbach
The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often obs…
Numerical methods for eigenvalues of singular polynomial eigenvalue problems
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were…
On the Convergence of the Gradient Descent Method with Stochastic Fixed-point Rounding Errors under the Polyak-Lojasiewicz Inequality
Lu Xia, Michiel E. Hochstenbach, Stefano Massei
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study…