Related papers: Multivariate Rational Approximation of Scattered D…
The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…
We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical systems. Its non-local structure requires taking into account the whole evolution history during the time integration, which then possibly causes…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical effectiveness of QR-AAA in a variety of computational…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on…
We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…
We introduce a theoretical framework for the rational approximation of optical response functions in resonant photonic systems. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems…
Ranking and selection (R&S) aims to identify the alternative with the best mean performance among $k$ simulated alternatives. The practical value of R&S depends on accurate simulation input modeling, which often suffers from the curse of…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…
This paper presents the Distributed Primal Outer Approximation (DiPOA) algorithm for solving Sparse Convex Programming (SCP) problems with separable structures, efficiently, and in a decentralized manner. The DiPOA algorithm development…