28 citations · 85 across the 30 of their papers we have counts for
32 papers
A Twin gradient method for unconstrained optimization
Anna De Magistris, Michiel E. Hochstenbach, Gerardo Toraldo
We propose a new strategy for gradient-based unconstrained optimization, involving two parallel sequences of iterates that cooperate to determine their stepsizes via a \textit{Twin…
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…
Solving singular generalized eigenvalue problems. Part III: structure preservation
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
In Parts I and II of this series of papers, three new methods for the computation of eigenvalues of singular pencils were developed: rank-completing perturbations, rank-projections…
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…
A subspace method for large-scale trace ratio problems
G. Ferrandi, M. E. Hochstenbach, M. R. Oliveira
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio.…
A DEIM-CUR factorization with iterative SVDs
Perfect Y. Gidisu, Michiel E. Hochstenbach
A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging.…
Limited memory gradient methods for unconstrained optimization
Giulia Ferrandi, Michiel E. Hochstenbach
The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review thi…
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…
Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models
Michiel E. Hochstenbach, Tomaž Košir, Bor Plestenjak
Standard multiparameter eigenvalue problems (MEPs) are systems of linear -parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems ha…
On the trace ratio method and Fisher's discriminant analysis for robust multigroup classification
Giulia Ferrandi, Igor V. Kravchenko, Michiel E. Hochstenbach +1
We compare two different linear dimensionality reduction strategies for the multigroup classification problem: the trace ratio method and Fisher's discriminant analysis. Recently,…
Block Discrete Empirical Interpolation Methods
Perfect Y. Gidisu, Michiel E. Hochstenbach
We present block variants of the discrete empirical interpolation method (DEIM); as a particular application, we will consider a CUR factorization. The block DEIM algorithms are ba…
Solving singular generalized eigenvalue problems. Part II: projection and augmentation
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing…
A homogeneous Rayleigh quotient with applications in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a ne…
A Restricted SVD type CUR Decomposition for Matrix Triplets
Perfect Y. Gidisu, Michiel E. Hochstenbach
We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets that aims to extract meaningful information by providing a low-rank approximation…
On the influence of stochastic roundoff errors and their bias on the convergence of the gradient descent method with low-precision floating-point computation
Lu Xia, Stefano Massei, Michiel E. Hochstenbach +1
When implementing the gradient descent method in low precision, the employment of stochastic rounding schemes helps to prevent stagnation of convergence caused by the vanishing gra…
A harmonic framework for stepsize selection in gradient methods
Giulia Ferrandi, Michiel E. Hochstenbach, Natasa Krejic
We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This provides…
A hybrid DEIM and leverage scores based method for CUR index selection
Perfect Y. Gidisu, Michiel E. Hochstenbach
The discrete empirical interpolation method (DEIM) may be used as an index selection strategy for formulating a CUR factorization. A notable drawback of the original DEIM algorithm…
A Generalized CUR decomposition for matrix pairs
Perfect Y. Gidisu, Michiel E. Hochstenbach
We propose a generalized CUR (GCUR) decomposition for matrix pairs . Given matrices and with the same number of columns, such a decomposition provides low-rank appr…
A Simple and Efficient Stochastic Rounding Method for Training Neural Networks in Low Precision
Lu Xia, Martijn Anthonissen, Michiel Hochstenbach +1
Conventional stochastic rounding (CSR) is widely employed in the training of neural networks (NNs), showing promising training results even in low-precision computations. We introd…
Improved stochastic rounding
Lu Xia, Martijn Anthonissen, Michiel Hochstenbach +1
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for diff…
A twin error gauge for Kaczmarz's iterations
Bart S. van Lith, Per Christian Hansen, Michiel E. Hochstenbach
We propose two new algebraic reconstruction techniques based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. Tomography problems exhibit semi…
Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched Backprojector
Yiqiu Dong, Per Christian Hansen, Michiel E. Hochstenbach +1
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backp…