Publications related to On multivariate trace inequalities of Sutter, Berta, and Tomamichel

Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice

The S=1 Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the S=3/2 AKLT model on the hexagonal lattice is also in a gapped phase has remained open, de ...

2020

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Kathryn Dianne Lund

We analyze an expansion of the generalized block Krylov subspace framework of [Electron.\ Trans.\ Numer.\ Anal., 47 (2017), pp. 100-126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and con ...

MATHICSE2019

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Volkan Cevher, Yen-Huan Li

Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...

2018

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

,

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

What do gravitons say about (unimodular) gravity?

Mario Herrero Valea

We revisit the problem of constraining the weak field limit of the gravitational lagrangian from S-matrix properties. From unitarity and Lorentz invariance of the S-matrix of massless gravitons, we derive on-shell gauge invariance to consist on the transve ...

SPRINGER2018

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

Daniel Kressner, Robert Gerhard Jérôme Luce, Francesco Statti

We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomia ...

MATHICSE2017

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Daniel Kressner, Robert Gerhard Jérôme Luce

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...

MATHICSE2016

Parallel algorithms for tensor completion in the CP format

Daniel Kressner, André Uschmajew

Low-rank tensor completion addresses the task of filling in missing entries in multidimensional data. It has proven its versatility in numerous applications, including context aware recommender systems and multivariate function learning. To handle large-sc ...

Elsevier Science Bv2016

Distinct Values Of Bilinear Forms On Algebraic Curves

Frank de Zeeuw, Adrian Claudiu Valculescu

Let B-M : C x C -> C be a bilinear form B-M(p, q) - p(T)Mq, with an invertible matrix M is an element of C-2x2. We prove that any finite set S contained in an irreducible algebraic curve C of degree d in C determines Omega(d)(vertical bar S vertical bar(4/ ...

Univ Calgary, Dept Math & Statistics2016

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

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Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Convergence of the Exponentiated Gradient Method with Armijo Line Search

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

What do gravitons say about (unimodular) gravity?

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Parallel algorithms for tensor completion in the CP format

Distinct Values Of Bilinear Forms On Algebraic Curves

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

What do gravitons say about (unimodular) gravity?

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

Parallel algorithms for tensor completion in the CP format

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice

Distinct Values Of Bilinear Forms On Algebraic Curves

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix