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We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…
Quantum phase estimation is an important component in diverse quantum algorithms. However, it suffers from spectral leakage, when the reciprocal of the record length is not an integer multiple of the unknown phase, which incurs an accuracy…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
We present a new explicit and stable numerical algorithm to solve the homogeneous heat equation. We illustrate the performance of the new method in the cases of two 2D systems with highly inhomogeneous random parameters. Spatial…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…
We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as…
Poisson's equation is the canonical elliptic partial differential equation. While there exist fast Poisson solvers for finite difference and finite element methods, fast Poisson solvers for spectral methods have remained elusive. Here, we…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…
A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The technique is motivated by the effectiveness of local nonlinear smoothers at overcoming strong…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal formulation transforms into multiplication in Fourier space and…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
We develop a fast and accurate method for 3D alignment, recovering the rotation and translation that best align a reference volume with a noisy observation. Classical matched filtering evaluates cross-correlation over a large discretized…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an…