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In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…
Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in…
In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
Approximate computing is an attractive paradigm for reducing the design complexity of error-resilient systems, therefore improving performance and saving power consumption. In this work, we propose a new two-level approximate logic…
This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
Recently, triple decomposition has attracted increasing attention for decomposing third-order tensors into three factor tensors. However, this approach is limited to third-order tensors and enforces uniformity in the lower dimensions across…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…