The Truncated Tracial Moment Problem

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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 ...

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

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This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

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In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

In this paper, we prove strong subconvexity bounds for self-dual GL(3) L-functions in the t-aspect and for GL(3) x GL(2) L-functions in the GL(2)-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pione ...

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 ...

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How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

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Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

The Truncated Tracial Moment Problem

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

Unlabeled Principal Component Analysis and Matrix Completion

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Preconditioning techniques for generalized Sylvester matrix equations

Tangent functional connectomes uncover more unique phenotypic traits

Emergence of Classical Magnetic Order from Anderson Towers: Quantum Darwinism in Action

On the uniqueness of solutions for the basis pursuit in the continuum

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

On the commutativity of flows of rough vector fields

Strong Subconvexity for Self-Dual GL(3) L-Functions

Iterative refinement of Schur decompositions

Optimal denoising of rotationally invariant rectangular matrices

Testing For The Rank Of A Covariance Operator

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Further results on latent discourse models and word embeddings

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Bootstrapping massive quantum field theories

Certified And Fast Computations With Shallow Covariance Kernels