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We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points. Firstly, we provide a…
Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…
We investigate superconvergence properties of the spectral interpolation involving fractional derivatives. Our interest in this superconvergence problem is, in fact, twofold: when interpolating function values, we identify the points at…
The multipole expansion method (MEM) is a spatial discretization technique that is widely used in applications that feature scattering of waves from circular cylinders. Moreover, it also serves as a key component in several other numerical…
Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
We propose modeling absorption spectrum measurements as mixtures of Gaussian process experts. This enables us to construct a flexible statistical model for interpolating and extrapolating measurements, facilitating statistical integration…
Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
The paper deals with the construction of images from visibilities acquired using aperture synthesis instruments: Fourier synthesis, deconvolution, and spectral interpolation/extrapolation. Its intended application is to specific situations…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
We present efficient methods to interpolate data with a quantum computer that complement uploading techniques and quantum post-processing. The quantum algorithms are supported by the efficient Quantum Fourier Transform (QFT) and classical…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…