Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...
The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...
In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...
This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...
The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...
Cosmological N-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistica ...
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...
This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and
considerations of statistical and com ...
We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...
Encapsulation techniques open up new possibilities to control the kinetics and location of the release of active ingredients. Despite the progresses achieved to obtain a better control over the dimensions and composition of the capsules, the encapsulation ...
