Related papers: A scaling and recovering algorithm for the matrix …
We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…
Matrix sensing has many real-world applications in science and engineering, such as system control, distance embedding, and computer vision. The goal of matrix sensing is to recover a matrix $A_\star \in \mathbb{R}^{n \times n}$, based on a…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
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…
$\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity (the size of the support set), under which with high probability a sparse signal…
The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
Personalised interactive systems such as recommender systems require selecting relevant items from massive catalogs dependent on context. Reward-driven offline optimisation of these systems can be achieved by a relaxation of the discrete…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
We study optimal algorithms in adaptive sampling recovery of smooth functions defined on the unit $d$-cube ${\II}^d:= [0,1]^d$. The recovery error is measured in the quasi-norm $\|\cdot\|_q$ of $L_q := L_q(\II^d)$. For $B$ a subset in…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…