Publications related to Power iteration

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Giuseppe Carleo, Riccardo Rossi, Clemens Giuliani, Filippo Vicentini

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...

Wien2023

Estimation of Self-Exciting Point Processes from Time-Censored Data

Thomas Alois Weber, Philipp Schneider

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observatio ...

2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

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 ...

SPRINGER2023

Analysis-aware defeaturing of complex geometries

Pablo Antolin Sanchez, Ondine Gabrielle Chanon

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

2022

Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems

Fabrizio Minganti

The characterization of open quantum systems is a central and recurring problem for the development of quantum technologies. For time-independent systems, an (often unique) steady state describes the average physics once all the transient processes have fa ...

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

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) ...

2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Nicolas Henri Bernard Flammarion, Aditya Vardhan Varre, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

2021

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Power iteration

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Estimation of Self-Exciting Point Processes from Time-Censored Data

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Covariance Estimation for Random Surfaces beyond Separability

Analysis-aware defeaturing of complex geometries

Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems

Robust Differentiable SVD

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

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

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Chat with Graph Search

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Estimation of Self-Exciting Point Processes from Time-Censored Data

Analysis-aware defeaturing of complex geometries

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

Covariance Estimation for Random Surfaces beyond Separability

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Robust Differentiable SVD