Randomized Block Gram–Schmidt Process for the Solution of Linear Systems and Eigenvalue Problems

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

The analysis of the acceleration behavior of gradient-based eigensolvers with preconditioning presents a substantial theoretical challenge. In this work, we present a novel framework for preconditioning on Riemannian manifolds and introduce a metric, the l ...

The deterministic errors of an accelerometer comprise the prevailing i) bias, ii) scale factor, and iii) non-orthogonality. Together, these errors result in a nonlinear measurement model, which is conventionally solved via an iterative nonlinear least-squa ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain non ...

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

Mapping the local microstructure properties of the tissue in the brain is crucial to understand any pathological condition from a biological perspective. In recent years, microstructure-imaging techniques aimed at extracting such precious information by us ...

In Control System Theory, the study of continuous-time, finite dimensional, underdetermined systems of ordinary differential equations is an important topic. Classification of systems in different categories is a natural initial step to the analysis of a g ...

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modele ...

The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In Fluid-Structure Interaction ...

Randomized Block Gram–Schmidt Process for the Solution of Linear Systems and Eigenvalue Problems

Chat with Graph Search

Riemannian acceleration with preconditioning for symmetric eigenvalue problems

Linear Estimation of Deterministic Accelerometer Errors

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Robust Differentiable SVD

Robust Controller Design For Linear Systems With Nonlinear Distortions: A Data-Driven Approach

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Accelerated Microstructure Imaging via Convex Optimization (AMICO) in crossing fibers

Finite Dimensional Methods for Differential Flatness

Linearization techniques for band structure calculations in absorbing photonic crystals

Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics