28 citations · 85 across the 30 of their papers we have counts for
9 papers · 1 filter
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…