Publications related to Fast Computation Of Spectral Projectors Of Banded Matrices

Learned Compressive Representations for Single-Photon 3D Imaging

Edoardo Charbon, Claudio Bruschini, Andrei Ardelean, Mohit Gupta

Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that ...

Ieee Computer Soc2023

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

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Antonio Joaquin Garcia Suarez

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 ...

2022

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 ...

SPRINGER2022

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

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Method of displaying an image on a see-through display

Sabine Süsstrunk, Adrien Birbaumer, Martinus Bosch

The present invention concerns a method of displaying an image on a see-through display. The method comprises: obtaining (101) a first electromagnetic radiation matrix of an object, the first matrix comprising first matrix elements representing radiation i ...

2019

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

SIAM PUBLICATIONS2019

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

Daniel Kressner, Stefano Massei

In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic proc ...

MATHICSE2019

Fast Computation Of Spectral Projectors Of Banded Matrices

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Learned Compressive Representations for Single-Photon 3D Imaging

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

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Iterative refinement of Schur decompositions

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

Construction of optimal spectral methods in phase retrieval

New Results in Integer and Lattice Programming

Method of displaying an image on a see-through display

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

New Results in Integer and Lattice Programming

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Learned Compressive Representations for Single-Photon 3D Imaging

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

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

Iterative refinement of Schur decompositions

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

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Method of displaying an image on a see-through display

Construction of optimal spectral methods in phase retrieval