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Concept

Tridiagonal matrix

Related publications (26)

Unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials

Nicola Marzari, Tommaso Chiarotti

Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel t ...

AMER PHYSICAL SOC2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

CovNet: Covariance networks for functional data on multidimensional domains

Victor Panaretos, Soham Sarkar

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 ...

WILEY2022

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

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 ...

SPRINGER2023

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

Momentum space CFT correlators for Hamiltonian truncation

Matthew Thomas Walters

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding ...

Springer Nature2020

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

Frédéric Mila, Bruce Normand

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S = 1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamilton ...

2018

Transient Data Processing of Flow Boiling Local Heat Transfer in a Multi-Microchannel Evaporator Under a Heat Flux Disturbance

John Richard Thome, Nicolas Lamaison, Houxue Huang

Multi-microchannel evaporators are often used to cool down electronic devices subjected to continuous heat load variations. However, so far, rare studies have addressed the transient flow boiling local heat transfer data occurring in such applications. The ...

Asme2017

A new method for reducing local heat transfer data in multimicrochannel evaporators

John Richard Thome, Navid Borhani, Nicolas Lamaison, Houxue Huang

Measuring the strong local variation in heat transfer coefficients in multi-microchannel evaporators is related to the inverse heat conduction problem (IHCP). As the local flow heat transfer coefficients change greatly in magnitude from single-phase liquid ...

Elsevier France-Editions Scientifiques Medicales Elsevier2017

Fast Computation Of Spectral Projectors Of Banded Matrices

Daniel Kressner, Ana Susnjara

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...

Siam Publications2017

A generalized definition of reactivity for ecological systems and the problem of transient species dynamics

Andrea Rinaldo, Lorenzo Mari

Perturbations to an ecosystem's steady state can trigger transient responses of great ecological relevance. Asymptotic stability determines whether a generic perturbation will fade out in the long run, but falls short of characterizing the dynamics imme ...

Wiley2017

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

Dominique Bonvin, Michael Amrhein, Julien Léo Billeter

Multivariate curve resolution via alternating least squares (ALS) is used to resolve the concentration profiles C and the pure component spectra E of S species from the multivariate absorbance data A, assuming the bilinear model ...

2016

Charge transport in superionic and melted AgI under a magnetic field studied via molecular dynamics

Sara Bonella

Charge transport in AgI subject to an external magnetic field is studied via computer simulations. We demonstrate that a recently developed algorithm can effectively complement problematic experiments to detect the ionic Hall effect, and identify previousl ...

Amer Physical Soc2016

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first

k

eigenvectors of the similarity matrix' Laplacian, whose computati ...

Ieee2016

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Nonadiabatic dynamics with intersystem crossings: A time-dependent density functional theory implementation

Ivano Tavernelli

In this work, we derive a method to perform trajectory-based nonadiabatic dynamics that is able to describe both nonadiabatic transitions and intersystem crossing events (transitions between states of different spin-multiplicity) at the same level of theor ...

Amer Inst Physics2015

Optimally Packed Chains of Bulges in Multishift QR Algorithms

Daniel Kressner

The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A. After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom right corner along ...

Association for Computing Machinery2014

On A Perturbation Bound For Invariant Subspaces Of Matrices