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Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…
We study structure-preserving Krylov subspace methods for approximating the matrix-vector products f(H)b, where H is a large Hamiltonian matrix and f denotes either the matrix exponential or the related phi-function. Such computations are…
The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
A class of linear parabolic equations are considered. We derive a common framework for the a posteriori error analysis of certain second-order time discretisations combined with finite element discretisations in space. In particular we…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…
As computational machines become larger and more complex, the probability of hardware failure rises. ``Silent errors'', or bit flips, may not be immediately apparent but can cause detrimental effects to algorithm behavior. In this work, we…
Markov Random Fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms.…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
In this thesis we propose a novel implementation of IDRstab that avoids several unlucky breakdowns of current IDRstab implementations and is further capable of benefiting from a particular lucky breakdown scenario. IDRstab is a very…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
The Arnoldi process provides an efficient framework for approximating functions of a matrix applied to a vector, i.e., of the form $f(M)\bm{b}$, by repeated matrix-vector multiplications. In this paper, we derive error estimates for…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability…
The need to estimate a positive definite solution to an overdetermined linear system of equations with multiple right hand side vectors arises in several process control contexts. The coefficient and the right hand side matrices are…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…