Related papers: Pole-fitting for complex functions: enhancing stan…
For large-scale computation of the exchange coupling constants $J_{ij}$, we reconstruct the Liechtenstein formula for localized orbital representation and simplify the energy integrations by adopting the finite pole approximation of the…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
This paper addresses optimal feedback selection for generic arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a structured system and a feedback cost matrix, our aim is to find a…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This problem is formulated for both continuous-time…
Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for…
Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the…
We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
We propose a novel sparse preference learning/ranking algorithm. Our algorithm approximates the true utility function by a weighted sum of basis functions using the squared loss on pairs of data points, and is a generalization of the kernel…
Matching theoretical predictions to experimental data remains a central challenge in hadron spectroscopy. In particular, the identification of new hadronic states is difficult, as exotic signals near threshold can arise from a variety of…
We show that it is possible to reduce a high-dimensional object like a neural network agent into a low-dimensional vector representation with semantic meaning that we call agent embeddings, akin to word or face embeddings. This can be done…
Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…